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Model&documentation&for:&
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Modelling&the&dynamics&of&Technological&Innovation&Systems&
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Bob"Walrave*,"Rob"Raven+"
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*"Eindhoven"University"of"Technology,"School"of"Industrial"Engineering,"Eindhoven,"The"
Netherlands"
+"Utrecht"University,"Copernicus"Institute,"Utrecht,"The"Netherlands&
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The"model"was"developed"in"Ventana"System’s"VENSIM"software."Figure"1"gives"an"
overview"of"the"full"model."The"model,"grounded"in"the"literature,"was"subjected"to"
robustness"analyses"and"served"to"run"the"different"scenarios"in"the"context"of"technological"
innovation"systems.""
Following"modelling"best"practices"(Holtz,"2011),"we"focus"only"on"one"part"the"
overarching"transition"dynamic."That"is,"rather"than"modelling"a"full"transition,"we"aim"to"
replicate"growth"(or"decline)"of"a"TIS"in"the"context"of"a"dominant"socio-technical"regime."As"
such,"the"‘goal’"of"any"given"simulation"is"to"arrive"at"the"state"where"the"‘Market"motor"
loop’"(R.5,"Figure"1)"grows"strong"enough"(i.e.,"generates"enough"resources)"to"drive"the"
whole"system,"independent"of"any"form"of"external"resources,"in"the"context"of"a"dominant"
socio-technical"regime."
The"six"loops"(Figure"1)"are"grounded"in"the"concept"of"motors"of"innovation"(Suurs,"
2009),"which"is"combined"with"the"notion"of"‘transition"pathways’"(Geels"and"Schot,"2007)."
These"six"feedback"loops,"which"are"discussed"in"the"manuscript,"are"presented"in"different"
colours"with"the"variable"names"written"in"black"(in"Figure"1)."The"green"variables"concern"
resources"that"are"being"fed"into"the"system—following"from"‘Fixed"external"resources’"
[Euro]"and/or"the"‘Niche"market’"[dmnl]"itself—needed"to"drive"the"system."The"brown"
variable"denotes"strong"exogenous"influences"(‘Landscape"pressure’"[dmnl]"and"‘Fixed"
external"resources’"[Euro])"on"the"system."The"orange"variables"indicate"adjustment"times"
(delays)"or"ratios."The"pink"constants"represent"resource"distribution"factors."The"purple"
variables"cause"for"random"variations"to"selected"flows."The"unit"of"time"in"the"model"is"
months"and"the"total"simulation"time"is"600"months."The"simulation"algorithm"is"Euler’s"
method"with"a"step"size"(dt)"of"0.0625"months."As"explained"in"the"manuscript,"the"model"
assumes"a"‘single"TIS"–"single"regime’"situation"and"is"not"attuned"to"a"technology-specific"
innovation"system."
The"main"ingredients"of"system"dynamics"models"are"stocks,"flows,"and"variables."In"
the"diagramming"notation,"stocks"are"represented"by"rectangles"and"denote"a"particular"
level"(e.g.,"the"amount"of"technological"knowledge"developed)."Flows"are"depicted"as"pipes"
with"valves"and"are"responsible"for"changes"(e.g.,"decrease"of"increase"of"the"technological"
knowledge)"in"the"stocks."Variables"are"those"constructs"that"are"dependent"on"stocks"and"
flows"(e.g.,"the"‘Resources"to"technology"development’)."Finally,"the"clouds"represent"
infinite"sources"or"outcomes"of"particular"flows"that"are"beyond"the"scope"of"the"model."
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"
"
Figure'1.'Overview'of'the'endogenous'model'structure.'
Regime
resistance loop
-"4"-"
MODEL&DESCRIPTION&
As"explained"in"the"manuscript,"the"model"is"composed"of"two"main"parts:"technology"
development"and"market"development."
Technology&development&
The&knowledge&development&motor&loop&–&Loop&B.1&
The"knowledge"development"motor"serves"as"prerequisite"for"innovation"processes"to"
occur."Activities"that"underlie"this"loop"are,"for"instance,"academic"studies"and"laboratory"
trials."Such"research"and"development"(R&D)"related"activities"constitute"a"source"of"
variation"to"the"system"(Suurs,"2009)"–"and"it"is"assumed"that"this"results"in"the"
development"of"a"certain"path-breaking"technology."We"capture"the"current"state-of-the-
art,"with"respect"to"technological"knowledge"developed,"by"the"stock"‘Technological"
knowledge"developed’"[dmnl]."(This"stock"thus"captures"all"the"knowledge,"distributed"over"
all"different"agents,"related"to"the"path-breaking"invention.)"This"stock"can"vary"between"0"
(lowest"level"="no"knowledge)"and"1"(highest"level"="a"nearly,"for"that"moment"in"time,"
‘complete’"understanding"of"the"technology)."
It"is"widely"acknowledged"that"the"improvement"of"technological"performance"
becomes"increasingly"more"difficult"once"that"technology"matures"and"starts"to"reach"it"
performance"limit"(De"Liso"&"Filatrella,"2008)."Indeed,"development"of"technological"
performance"typically"follows"a"S-shaped"growth"curve"over"time"(Christensen,"1992a,"
1992b;"Schilling"&"Esmundo,"2009;"Suurs,"2009)."We"adopt"this"conception"in"our"model"by"
making"technological"progress"increasingly"difficult"the"higher"the"state"of"
development/diffusion."More"specifically,"increasingly"more"resources"are"needed"to"
achieve"technological"performance"growth,"the"higher"the"state-of-the-art."In"this"respect,"
growth"in"this"part"of"the"system"is"bounded"by"a"performance"ceiling."This"makes"these"two"
loops"‘goal-seeking’"in"nature."
If,"for"some"reason,"knowledge"development"stops"(or"is"severely"limited),"the"
current"body"of"knowledge"becomes"obsolete"over"time"(due"to"new"technological"
developments,"etc.)."As"such,"the"‘Technological"knowledge"developed’"[dmnl]"stock"is"
subject"to"an"outflow,"called"‘Knowledge"decay"rate’"[dmnl/month]."Here"we"assume"an"
exponential"decay"structure"(Sterman,"2000)"(i.e.,"knowledge"decreases"at"a"rate"
-"5"-"
proportional"to"its"current"value:"The"more"knowledge"there"is,"the"more"knowledge"is"
subject"to"becoming"out-dated)."As"such,"we"adopt"an"adjustment"time"(Sterman,"2000)"
given"by"the"constant"‘Knowledge"decay"time’"[month]."Equation"1"captures"the"behaviour"
of"the"knowledge"decay"rate"(where"the"‘Knowledge"development"rate’"[dmnl/month]"is"
given"in"Equation"2)."
(1)$Knowledge$decay$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$–$Technological$$knowledge$developed$/$
Knowledge$decay$time$[+$Knowledge$development$rate]$
"
Vice"versa,"due"to"investments"in,"for"instance,"R&D"(captured"by"the"variable"
‘Resources"to"R&D’"[Euro]),"the"stock"‘Technological"knowledge"developed’"[dmnl]"
increases."This"increase"is"captured"by"the"inflow"‘Knowledge"development"rate’"
[dmnl/month]."Here,"we"assume"an"exponential"growth"structure."That"is,"we"assume"that"
improvement"of"technological"performance"becomes"progressively"more"difficult"once"that"
technology"matures"and"starts"to"reach"it"performance"limit"(De"Liso"and"Filatrella,"2008)."
This"growth"characteristic"is"captured"by"Equation"2,"by"the"introduction"of"an"adjustment"
time"(i.e.,"the"‘AT"TKDe’"[month])"in$combination$with"a"increasingly"limited"potential"
maximum"‘Technological"knowledge"developed’"(i.e.,"1"–"‘Technological"knowledge"
developed’)."This"setup"allows"the"stock"‘Technological"knowledge"developed’"to"follow"a"S-
shaped"growth"curve,"typical"for"technological"developments"(Christensen,"1992a,"1992b;"
Schilling"and"Esmundo,"2009;"Suurs,"2009)."Subsequently,"we"calculate"the"inflow"as"given"in"
Equation"2—where"the"constant"‘Euro"to"knowledge"development"rate’"[dmnl/Euro]"
captures"how"much"knowledge"is"(initially)"gained"per"invested"Euro—and"where"the"
‘Knowledge"decay"rate’"[dmnl/month]"is"presented"in"Equation"1."
(2)$Knowledge$development$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$+$((1$-$Technological$knowledge$developed)$*$
(Resources$to$R&D$*$Euro$to$knowledge$development$rate))$/$AT$TKDe$[–$Knowledge$decay$
rate]$
"
The"stock"‘Technological"knowledge"developed’"[dmnl]"(partially)"determines"the"
levels"of"the"stocks"‘Guidance"of"the"search’"[dmnl]"and"‘Resource"mobilization’"[Euro]."As"
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can"be"seen"in"Figure"1,"these"stocks"are"also"part"of"‘The"knowledge"diffusion"motor’"(loop"
B.2)"and,"therefore,"are"discussed"in"the"next"section."The"latter"stock"captures"the"total"
amount"of"resources"(in"Euro’s)"put"to"use"for"both"technology"development"and"diffusion."
In"this"respect,"a"certain"percentage"of"the"available"budget"(denoted"by"‘Knowledge"
resource"distribution’"[dmnl—%])"is"made"available"to"knowledge"development,"while"the"
rest"(i.e.,"1"–"‘Knowledge"resource"distribution’)"is"directed"toward"knowledge"diffusion."
Subsequently,"the"‘Resources"to"R&D’"[Euro]"can"be"calculated"as"in"Equation"3."
(3)$Resources$to$R&D$[Euro]$=$Knowledge$resource$distribution$*$Resource$mobilization$
"
The"‘Resources"to"R&D’"[Euro]"subsequently"drives"the"already"discussed"‘Knowledge"
development"rate’"[dmnl/month]."As"such,"this"completes"the"description"of"the"balancing"
‘Knowledge"development"motor"loop’"(loop"B.1)."
The&knowledge&diffusion&motor&loop&–&Loop&B.2&
In"order"for"the"technology"and"a"market"to"develop,"the"developed"technological"
knowledge"need"to"diffuse"among"relevant"actors"(through,"e.g.,"conferences,"workshops,"
and"alliances)."We"capture"the"current"state"of"knowledge"diffused"with"the"stock"
‘Technological"knowledge"diffused’"[dmnl]."This"stock"also"varies"between"0"(implying"no"
technological"knowledge"is"diffused)"and"1"(meaning"that"nearly"all"currently$available"
technological"knowledge"is"diffused)."This"stock"is"also"subject"to"exponential"decay"due"to"
knowledge"loss"over"time,"which"is"captured"by"the"‘Knowledge"loss"rate’"[dmnl/month],"
with"adjustment"time"‘Knowledge"decay"time’"[month]."Furthermore,"if"new"knowledge"is"
developed"(i.e.,"a"positive"‘Knowledge"development"rate’"[dmnl/month]),"the"level"of"
‘Technological"knowledge"diffused’"[dmnl]"should,"pro-rata,"decrease."This"then"results"in"
Equation"4—where"the"‘Knowledge"diffusion"rate’"[dmnl/month]"is"explained"by"Equation"5."
(4)$Knowledge$loss$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$–$(Technological$knowledge$diffused$/$
Knowledge$decay$time)$–$(Technological$knowledge$diffused$*$(Knowledge$development$rate$
/$Technological$knowledge$developed))$[+$Knowledge$diffusion$rate]$
"
The"level"of"‘Technological"knowledge"diffused’"[dmnl]"increases"through"
investments"(captured"by"the"variable"‘Resources"to"knowledge"diffusion’"[Euro]"–"see"
-"7"-"
Equation"6)."Similar"to"the"structure"underlying"the"‘Knowledge"development"rate’"
[dmnl/month],"we"assume"that"it"becomes"progressively"more"difficult"to"make"progress"
and,"as"such,"introduce"an"adjustment"time"‘AT"TKDi’"[month]"in"combination"with"a"
increasingly"limited"potential"maximum"‘Knowledge"diffusion"rate’"[dmnl/month]"(i.e.,"1$–$
‘Technological$knowledge$diffused’)."Equation"5"captures"this"–"where"the"constant"‘Euro"to"
knowledge"diffusion"rate’"[dmnl/Euro]"denotes"how"much"knowledge"is"(initially)"gained"per"
invested"Euro—and"where"the"‘Knowledge"loss"rate’"[dmnl/month]"is"given"in"Equation"4."
(5)$Knowledge$diffusion$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$+$((1$–$Technological$knowledge$diffused)$*$
(Resources$to$knowledge$diffusion$*$Euro$to$knowledge$diffusion$rate))$/$AT$TKDi$[–$
Knowledge$loss$rate]$
"
Following"the"logic"underlying"Equation"3,"the"‘Resources"to"knowledge"diffusion’"
[Euro]"can"be"calculated"as"follows"(Equation"6)."
(6)$Resources$to$knowledge$diffusion$[Euro]$=$(1$–$Knowledge$resource$distribution)$*$
Resource$mobilization$
"
‘Technological"knowledge"developed’"and"‘Technological"knowledge"diffused’"shape"
the"‘guidance"of"the"search’."For"example,"the"successful"realisation"of"a"research"project,"
contributing"to"‘Technological"knowledge"developed’"and/or"to"'Technological"knowledge"
diffused’"can"result"in"high"expectations"which"contributes"to"the"function"‘Guidance"of"the"
Search’"(Suurs"and"Hekkert,"2012)."As"such,"we"consider"the"interaction"between"the"
‘Technological"knowledge"diffused’"[dmnl]"and"the"‘Technological"knowledge"developed’"
[dmnl]"to"reflect"the"status"of"such"shared"development"vision,"influencing"how"effectively"
the"‘Resources"to"technology"development’"can"be"utilized."Yet,"we"consider"only"a"certain$
percentage"(i.e.,"captured"by"the"constant"‘Effectiveness"and"efficiency"factor"funding’"
[dmnl—%])"of"all"available"resources"for"technology"development"(i.e.,"‘Resources"to"
technology"development’"[Euro])"to"be"subject"such"the"interaction—as"in"Equation"7,"
where"‘AT"GoS’"[month]"is"the"adjustment"time:"
"
"
-"8"-"
(7)$Change$in$Guidance$of$the$Search$[Euro/month]:$
d$(Guidance$of$the$Search)$/$dt$=$((Technological$knowledge$developed$*$Technological$
knowledge$diffused$*$Effectiveness$and$efficiency$factor$*$Resources$to$technology$
development$+$(1$–$Effectiveness$and$efficiency$factor)$*$Resources$to$technology$
development)$–$Guidance$of$the$Search)$/$AT$GoS$
"
Furthermore,"as"there"is"a"time"delay"between"the"accreditation"of"resources"and"the"
actual"resource"division"and"utilization"(i.e.,"‘Resource"mobilization’"[Euro]),"we"utilize"a"
simple"first-order"adaptive"structure"(Sterman,"2000)"for"calculating"the"change"to"‘Resource"
mobilization’"[Euro]."As"such,"we"can"describe"Equation"8"–"where"‘AT"RM’"[month]"denotes"
the"adjustment"time:"
(8)$Change$in$Resource$mobilization$[Euro/month]:$
d$(Resource$mobilization)$/$dt$=$(Guidance$of$the$search$–$Resource$mobilization)$/$AT$RM$
"
The"‘Resources"to"knowledge"diffusion’"[Euro]"drives"the"already"discussed"
‘Knowledge"diffusion"rate’"[dmnl/month]."This"then"completes"the"description"of"the"
balancing"‘Knowledge"diffusion"motor"loop’"(loop"B.2)."
Market&development&
The&entrepreneurial&motor&loop&–&Loop&R.3&
The"manuscript"outlines"that"the"‘Perceived"legitimacy"of"the"TIS’"is"dependent"on"both"
technological"legitimacy"and"market"legitimacy."We"consider"the"interaction"between"
‘Technological"knowledge"developed’"[dmnl]"and"‘Technological"knowledge"diffused’"[dmnl]"
to"represent"such"for"former"type"of"legitimacy."This"latter"type"of"legitimacy"follows"from"
(a)"the"level"of"‘TIS"structures’"[dmnl];"which"positively"influences"the"legitimacy—see"
Equation"16);"and"(b)"the"level"of"‘Regime"resistance"toward"TIS’"[dmnl],"negatively"
influencing"the"legitimacy—see"Equation"24)."The"perceived"technological"legitimacy"and"
perceived"market"legitimacy"combined"determine"the"stock"‘Perceived"legitimacy"of"the"TIS’"
[dmnl]."This"stock"can"vary"between"0"(no"legitimacy)"to"1"(full"legitimacy)."
In"general,"perceptions"adjust"to"new"circumstances"with"a"certain"delay,"which"can"
be"modelled"in"terms"of"the"behaviour"of"a"first-order"adaptive"system"(Sterman,"2000)."As"
-"9"-"
such,"we"model"change"to"the"stock"‘Perceived"legitimacy"of"the"TIS’"[dmnl]"as"a"first-order"
adaptive"system,"in"Equation"9,"with"adjustment"time"‘AT"PLT’"[month]."
(9)$Change$in$Perceived$legitimacy$of$the$TIS$[dmnl/month]:$
d$(Perceived$legitimacy$of$the$TIS)$/$dt$=$((Technological$knowledge$diffused$*$Technological$
knowledge$developed$*$TIS$structures$*$(1$–$Regime$resistance$toward$TIS))-Perceived$
legitimacy$of$the$TIS$)$/$AT$PLT$
"
The"stock"‘Entrepreneurial"activity’"[dmnl]"represents"the"number"of"firms"and"
entrepreneurs"becoming"active"in"the"innovation"system."This"stock,"like"the"formerly"
described"stocks,"also"varies"between"0"(implying"no"entrepreneurial"activity)"and"1"
(meaning"full"‘saturation’"with"respect"to"entrepreneurial"activity)."
The"stock"‘Entrepreneurial"activity’"[dmnl]"is"expected"to"change,"with"a"certain"
delay,"as"the"result"of"change"within"the"‘Perceived"legitimacy"of"the"TIS’"[dmnl]."As"
explained"in"the"manuscript,"we"assume"a"non-linear"relationship,"which"is"modelled"by"
means"of"a"so-called"lookup"function"(denoted"by"the"lookup"variable"‘Effect"of"PLT"on"EA’)."
This"relationship"is"depicted"in"Figure"2."This"relation"thus"follows"a"‘band-wagon"effect’"
(Geels,"2005),"where"the"rate$of$change"in"entrepreneurial"activity"increases"the"more"
entrepreneurial"activity"is"installed.""
"
"
0""""""""""""""""""""0.25"""""""""""""""""""0.5"""""""""""""""""""0.75"""""""""""""""""""1"
Perceived"legitimacy"of"the"TIS"
Figure&3.&Non-linear&relation&between&‘Perceived&legitimacy&of&the&TIS’&and&
‘Entrepreneurial&activity’.&
0
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0
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0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
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0.8
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0.9
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1
Entrepreneurial activity
Perceived legitimacy of the TIS
1"
"
.75"
"
.5"
"
.25"
"
0"
Entrepreneurial"activity"
-"10"-"
Entrepreneurial"activity"can,"furthermore,"be"spurred"by"external"actors,"for"
instance,"by"external"agents"approaching"firms"and"research"institutes"to"participate"in"
development"initiatives"aimed"at"the"realization"of"pilots"and"demonstrations."In"this"
respect,"it"is"very"likely"that"for"instance"governments,"aiming"to"expedite"the"development"
and"introduction"of"the"socially"desirable"new"technology"and"belonging"solutions"(e.g.,"
more"sustainable),"are"backing"entrepreneurs"with"project"specific"subsidies"(Suurs,"2009)."
This"reduces"perceived"entrepreneurial"risks—effectively"resulting"in"more"‘Entrepreneurial"
activity’"[dmnl]"respective"to"the"current"level"of"‘Perceived"legitimacy"of"the"TIS’"[dmnl]."We"
modelled"this"by"introducing"the"variable"‘Effect"funding"on"PLT’"[dmnl]"(see"Equation"11)"
within"the"lookup"section"of"Equation"10."Equation"10"captures"the"described"dynamics—
with"adjustment"time"‘AT"EI’."(Note"that"growth"in"‘Entrepreneurial"activity’"[dmnl]"is"
bounded"by"the"‘1"–"Entrepreneurial"activity’"term.)"
(10)$Entrepreneurial$interest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$+$((1$–$Entrepreneurial$activity)$*$(Effect$of$PLT$on$EA$
(Perceived$legitimacy$of$the$TIS$+$Effect$funding$on$PLT))$/$AT$EI$[–$Entrepreneurial$
disinterest$rate]$
"
In"this"respect,"following"equation"11,"the"variable"‘Effect"funding"on"PLT’"[dmnl]"
effectively"converts"the"amount"of"resources"available"to"stimulate"‘Entrepreneurial"activity’"
[dmnl]"(i.e.,"‘Funding"EA’"[Euro],"see"Equation"23)"to"an"increase"in"the"level"of"‘Perceived"
legitimacy"of"the"TIS’"[dmnl],"through"introduction"of"the"constant"‘Euro"to"change"in"PLT’"
[dmnl/Euro]."For"model"robustness,"we"limit"the"maximum"outcome"of"Equation"11"to"1"by"
means"of"a"so-called"‘MIN’"statement.""
(11)$Effect$funding$on$PLT$[dmnl]$=$MIN$(Euro$to$change$in$PLT$(Funding$EA),$1)$
"
Yet,"if"the"‘Perceived"legitimacy"of"the"TIS’"[dmnl]"drops,"so"does"entrepreneurial"
interest"in"the"TIS—albeit"with"a"certain"delay."We"adopt"an"exponential"decay"structure"to"
model"this;"with"adjustment"time"‘AT"EDI’"[month],"as"presented"by"Equation"12."
(12)$Entrepreneurial$disinterest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$–$Entrepreneurial$activity$/$AT$EDI$[+$Entrepreneurial$
interest$rate]$
-"11"-"
As"‘Entrepreneurial"activity’"[dmnl]"increases,"so"do"the"resources"provided"to"
further"system"development,"as"initial"entrepreneurial"profits"feedback"into"the"system."We"
model"this"through"introducing"the"constant"‘Variable"input"percentage’"[dmnl—%],"which"
makes"a"part"of"the"total"amount"of"external"resources"(i.e.,"‘Fixed"external"resources’"
[Euro],"see"the"section"‘Exogenous"inputs’)"dependent"on"the"level"of"‘Entrepreneurial"
activity’"[dmnl]."Equation"13"details"the"mechanism."
(13)$External$resources$[Euro]$=$(1$–$Variable$input$percentage)$*$Fixed$external$resources$+$
Variable$input$percentage$*$Fixed$external$resources$*$Entrepreneurial$activity$
"
The"resources"are"subsequently"distributed"over"technology"development—through"
‘Funding"technology"development"(External"resources)’"[Euro]—and"market"development—
‘Funding"market"development"(External"resources)’"[Euro],"through"a"given"percentage"
(denoted"by"‘External"resources"distribution’"[dmnl—%])."From"here,"we"can"describe"
Equation"14"and"15."
(14)$Funding$technology$development$(External$resources)$[Euro]$=$External$resources$*$
External$resources$distribution$
"
(15)$Funding$market$development$(External$resources)$[Euro]$=$External$resources$*$(1$–$
External$resources$distribution)$
"
The"‘Funding"technology"development"(External"resources)’"[Euro]"(Equation"14)"
subsequently"serves,"partly,"as"input"for"the"variable"‘Resources"to"technology"development’"
[Euro]"(see"Equation"22),"which"in"its"turn"feeds"into"‘Resource"mobilization’"[Euro]"
(Equation"8)."The"resources"for"market"development"(i.e.,"Equation"15)"are"further"split"into"
resources"directed"to"stimulate"entrepreneurial"activity"(i.e.,"‘Funding"EA’"[Euro],"Equation"
23);"and"funds"directed"to"stimulate"growth"in"TIS"structures"(i.e.,"‘Funding"TISS’"[Euro],"
Equation"24)—see"section"on"the"‘Market"motor"loop’"(loop"R.5)."As"such,"this"completes"
the"description"of"the"reinforcing"‘Entrepreneurial"motor"loop’"(loop"R.3)."
"
-"12"-"
The&system&building&motor&loop&–&Loop&R.4&
As"argued"in"the"manuscript,"as"‘Entrepreneurial"activity’"[dmnl]"increases,"‘TIS"structures’"
[dmnl]"arise."The"‘TIS"structures’"[dmnl]"is"modelled"as"a"stock,"and"can"vary"between"0"(no"
TIS"structures)"and"1"(a"‘complete’"set"of"TIS"structures)."We"assume"that"the"influence"of"
entrepreneurs"on"the"formation"processes"of"‘TIS"structures’"[dmnl]"becomes"increasingly"
large"as"‘Entrepreneurial"activity’"[dmnl]"increases—reflecting"the"need"for"a"certain"critical$
mass"before"substantial"influence"can"be"exercised."We"model"this"relation"between"
‘Entrepreneurial"activity’"[dmnl]"and"‘TIS"structures’"[dmnl]"through"a"lookup"function;"
denoted"by"the"variable"‘Effect"of"EA"on"TISS’"[dmnl]"and"depicted"in"Figure"3."
"
"
0""""""""""""""""""""0.25"""""""""""""""""""0.5"""""""""""""""""""0.75"""""""""""""""""""1"
Entrepreneurial"activity"
Figure&4.&Non-linear&relation&between&‘Entrepreneurial&activity’&and&‘TIS&structures’.&
"
Other"actors"can"also"stimulate"the"development"of"‘TIS"structures’"[dmnl]."For"
instance,"governments"can"support"the"building"of"institutions"by"introducing"new"
environmental"standards"fit"to"the"emerging"TIS"(Suurs,"2009)."We"model"this"influence"by"
introducing"the"variable"‘Effect"funding"on"TISS’"[dmnl/Euro]"in"Equation"16,"which"serves"to"
translate"the"input"that"originates"from"the"variable"‘Funding"TISS’"[Euro]"(see"Equation"24)"
into"an"increase"in"the"‘TIS"structures’"[dmnl]."Note"that,"once"more"for"model"robustness,"
we"limit"the"potential"‘Effect"funding"on"TISS’"[dmnl]"to"1"by"means"of"a"‘MIN’"statement."
From"here,"we"can"define"Equations"16"and"17."
"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Formal institutions and systems
Entrepreneurial activity
1"
"
.7
5"
"
.5"
"
.2
5"
TIS"structures"
-"13"-"
(16)$Change$in$TIS$structures$[dmnl/month]:$
d$(TIS$structures)$/$dt$=$(1$–$TIS$structures)$*$((Effect$of$EA$on$TISS$(Entrepreneurial$activity)$+$
Effect$funding$on$TISS)$–$TIS$structures)$/$AT$TISS$
"
$(17)$Effect$funding$on$TISS$[dmnl/Euro]$=$MIN$(Euro$to$change$in$TISS$*$Funding$TISS,$1)$
"
The"existence"of"‘TIS"structures’"[dmnl]"influences"the"further"development"of"the"TIS"
in"two"manners:"First,"the"existence"of"FIS"provides"face"validity"for"the"emerging"
technology,"directly"influencing"the"‘Perceived"legitimacy"of"the"TIS’"[dmnl]"(see"Equation"9)."
Furthermore,"the"existence"of"‘TIS"structures’"[dmnl]"negatively"influences"the"‘Regime"
resistance"toward"TIS’"[dmnl]"as"broadening"networks"and"the"establishment"of"
intermediaries"enforce"growth"of"the"emerging"niche"market,"thereby"counteracting"regime"
resistance."Also"see"Equation"25."This"concludes"the"discussion"on"the"reinforcing"‘System"
building"motor"loop’"(loop"R.4)."
The&market&motor&loop&–&Loop&R.5&
As"explained"in"the"manuscript,"growth"in"‘Entrepreneurial"activity’"[dmnl]"also"results,"
albeit"with"a"delay"(‘AT"NM’"[month]),"in"‘Niche"market’"[dmnl]"growth"(once"more,"we"
adopt"a"first-order"adaptive"system)."Yet,"the"‘Niche"market’"[dmnl]"can"only"truly"develop"
when"innovation"system"actors"successfully"navigate"the"creation"of"‘TIS"structures’"[dmnl]."
As"such,"we"consider"the"interaction"between"‘Entrepreneurial"activity’"[dmnl]"and"‘TIS"
structures’"[dmnl]"to"indicate"change"in"the"‘Niche"market’"[dmnl]—See"Equation"18."
(18)$Change$in$Niche$market$[dmnl/month]:$
d$(Niche$market)$/$dt$=$((Entrepreneurial$activity$*$TIS$structures)$–$Niche$market)$/$AT$NM$
"
The"reinforcing"‘Market"motor"loop’"(loop"R.5)"can,"once"dominant,"sustain"all"other"
motors"(albeit"that"this"requires"a"rather"large"‘Niche"market’),"by"generating"‘Niche"input’"
[Euro]"to"the"funds"going"into"technology"development."In"such"situation,"there"is"no"need"
for"‘External"resources’"[Euro]"anymore,"as"a"self-sustaining"TIS"has"been"created."The"size"of"
the"variable"‘Niche"input’"[Euro]"is"determined"by"multiplying"the"size"of"the"‘Niche"market’"
[dmnl]"with"the"constant"‘Niche"to"Euro"factor’"[Euro/dmnl]—as"in"Equation"19."
"
-"14"-"
(19)$Niche$input$[Euro]$=$Niche$to$Euro$factor$*$Niche$market$
"
Subsequently,"the"available"resources,"following"from"the"‘Niche"market’"[dmnl]"are"
distributed"over"technology"development"and"market"development."The"constant"‘Niche"
input"distribution’"[Dmnl—%]"determines"this"division;"similar"to"the"constant"‘External"
resources"distribution’—see"Equations"14"and"15."From"here,"we"formulate"Equations"20"
and"21."
(20)$Funding$technology$development$(Niche)$[Euro]$=$Niche$input$*$(Niche$input$
distribution)$
"
(21)$Funding$market$development$(Niche)$[Euro]$=$Niche$input$*$(1$–$Niche$input$
distribution)$
"
The"‘Funding"technology"development"(Niche)’"[Euro]"(Equation"20)"and"the"‘Funding"
technology"development"(External"resources)’"[Euro]"(Function"14)"determine"the"variable"
‘Resources"to"technology"development’"[Euro]"(which"serves"as"input"for"Equation"8),"as"
described"by"Equation"22."
(22)$Resources$to$technology$development$[Euro]$=$Funding$technology$development$
(External$resources)$+$Funding$technology$development$(Niche)$
"
The"resources"following"from"‘Funding"market"development"(External"resources)’"
[Euro]"and"from"‘Funding"market"development"(Niche)’"[Euro]"are"utilized"for"the"
development"of"‘Entrepreneurial"activity’"[dmnl]"and"‘TIS"structures’"[dmnl]."We"do"so"by"
introducing"two"constants:"(1)"‘Market"resource"distribution"(External"resources)’"[dmnl—
%],"and"(2)"‘Market"resource"distribution"(Niche)’"[dmnl—%]."This"results"in"Equations"23"
and"24—which"feed"into"Equations"11"and"17."
(23)$Funding$EA$[Euro]$=$Funding$market$development$(External$resources)$*$Market$
resource$distribution$(External$resources)$+$Funding$market$development$(Niche)$*$Market$
resource$distribution$(Niche)$$
"
-"15"-"
(24)$Funding$TISS$[Euro]$=$Funding$market$development$(External$resources)$*$(1$–$Market$
resource$distribution$(External$resources))$+$Funding$market$development$(Niche)$*$(1$–$
Market$resource$distribution$(Niche))$
$
This"concludes"the"description"of"the"reinforcing"‘Market"motor"loop’"(loop"R.5)."
The®ime&resistance&loop&–&Loop&B.6&
The"final"loop"in"the"model"is"the"‘Sailing"ship"loop’"(B.6)."This"loop"is"added"to"the"existing"
TIS"framework"to"account"for"the"potential"feedback"loops"between"a"TIS"and"its"context."
First,"the"growth"of"a"TIS"‘Niche"market’"[dmnl]"triggers"the"‘Sailing"ship"effect’"[dmnl],"which"
implies"an"increase"in"the"‘Regime"resistance"toward"TIS’"(ranging"from"0-1:"0"implying"no"
selection"pressure"at"all,"1"means"a"severe"selection"environment;"i.e.,"no"‘Niche"market’"
[dmnl]"can"develop—see"Equation"9)."The"stock,"model"as"a"first-order"adaptive"system,"is"
subject"to"adjustment"time"‘AT"RRT’"[month]."
As"explained,"we"assume"that"the"development"of"‘TIS"structures’"[dmnl]"lowers"the"
‘Regime"resistance"toward"TIS’"[dmnl]."In"order"to"control"for"the"effect"that"‘TIS"structures’"
[dmnl]"has"on"‘Regime"resistance"toward"TIS’"[dmnl],"we"introduce"the"constant"‘Effect"FIS"
on"RRT’"[dmnl—%]."More"specifically,"this"latter"constant"causes"that"a"fully"developed"‘TIS"
structures’"[dmnl]"diminishes"the"‘Regime"resistance"toward"TIS’"[dmnl]"to"a"certain"
degree—rather"then"completely"(this"is"in"line"with"our"aim"to"replicate"growth/decline"of"a"
TIS"in"the"context"of"a"dominant"regime,"rather"than"modelling"a"full"transition)."Yet,"
simultaneously,"due"to"‘Niche"market’"[dmnl]"growth"the"‘Regime"resistance"toward"TIS’"
[dmnl]"increases"as"a"result"of"the"‘Sailing"ship"effect’"[dmnl]"(De"Liso"and"Filatrella,"2008)."
Note"that,"in"Equation"25,"we"bounded"growth"to"the"stock"‘Regime"resistance"
toward"TIS’"[dmnl]"to"1—by"means"of"a"‘MIN’"statement."The"assumed"persistence"of"the"
‘Sailing"ship"effect’"[dmnl],"in"combination"with"a"decline"in"the"‘TIS"structures’"[dmnl]"(as"
the"result"of"a"failing"TIS)"can,"without"such"‘MIN’"statement,"result"in"the"situation"where"
the"‘Regime"resistance"toward"TIS’"grows"larger"than"the"theoretically"possible"value"of"1"
(and"compromise"model"robustness).""
Finally,"the"‘Regime"resistance"toward"TIS’"[dmnl]"is"subject"to"‘Landscape"pressure’"
[dmnl]—see"section"on"‘Exogenous"inputs’."Such"influences"(e.g.,"oil"price"changes,"climate"
change,"etc.)"put"significant"pressure"on"the"currently"dominant"regime"(Suurs,"2009),"
-"16"-"
causing"a"drop"in"the"‘Regime"resistance"on"TIS’"[dmnl]."As"such,"we"can"model"change"in"the"
‘Regime"resistance"toward"TIS’"[dmnl]"as"follows"(Equation"25)."
(25)$Change$in$the$Regime$resistance$toward$TIS$[dmnl/month]:$
d$(Regime$resistance$toward$TIS)$/$dt$=$(MIN$(1$–$TIS$structures$*$Effect$FIS$on$RRT$+$Sailing$
ship$effect$–$Landscape$pressure,$1)$–$Regime$resistance$toward$TIS)$/$AT$RRT$
"
The"modelled"‘Sailing"ship"effect’"can"be"described"in"the"following"manner:"
phase"A) Initially,"the"‘Sailing"ship"effect’"will"build"up"as"a"result"of"‘Niche"market’"
[dmnl]"growth."
phase"B) Subsequently,"once"a"certain"‘Niche"market’"[dmnl]"size"has"been"crossed,"
the"‘Sailing"ship"effect’"will"retain"its"maximum"effect"size"(and"not"grow"
any"stronger)."
phase"C) Then,"if"the"‘Niche"market’"[dmnl]"has"been"able"to"keep"a"certain"size,"for"
a"given"amount"of"time,"the"‘Sailing"ship"effect’"declines"again."
As"such,"in"order"to"determine"the"‘Sailing"ship"effect’"[dmnl],"two"elements"of"the"
‘Niche"market’"[dmnl]"need"to"be"captured:"First,"its"historically"largest"size."And"second,"the"
duration"the"‘Niche"market’"[dmnl]"exceeded"a"certain"assumed"threshold"size."That"is,"the"
sailing"ship"effect"is"not"likely"to"last"indefinitely"and,"as"such,"a"niche"market,"exceeding"a"
certain"size"(captured"by"the"constant"‘Size"threshold"SSE’"[dmnl])"for"a"given"amount"of"
time"(captured"by"the"constant"‘Duration"threshold"SSE’"[month]),"is"likely"to"overcome"the"
‘Sailing"ship"effect’"[dmnl]."
For"the"former"element,"we"introduce"the"stock"‘Historically"largest"niche"market’"
[dmnl],"which"records"the"historically"largest"‘Niche"market’"as"a"one-way"adaptive"system"
(implying"the"stock"can"never"decline)"with"no"delay"(adjustment"time"equals"‘Time"Step’)."
As"in"Equation"26."
(26)$Change$in$Historically$largest$Niche$market$[dmnl]:$
d$(Historically$largest$Niche$market)$/$dt$=$IF$THEN$ELSE$(Historically$largest$niche$market$<$
Niche$market,$(Niche$market$–$Historically$largest$niche$market)$/$TIME$STEP,$0)$
"
The"latter"element"is"captured"by"the"stock"‘Duration"above"threshold’"[Month]"
(once"more,"an"one-way"adaptive"system"with"no"delay),"which"keeps"track"of"the"amount"
-"17"-"
of"months"the"‘Niche"market’"exceeded"the"given"‘Size"threshold"SSE’"[Dmnl]—as"described"
by"Function"27."
(27)$Change$in$Duration$above$threshold$[month]:$
d$(Duration$above$threshold)$/$dt$=$IF$THEN$ELSE$(Niche$market$>$Size$threshold$SSE,$1,$0)$/$
TIME$STEP$
"
Equation"26"and"27"combined"determine"the"‘Sailing"ship"effect’"[dmnl]"(following"
the"outlined"reasoning)."In"order"to"do"so,"we"first"determine"the"‘SSE"status’"[dmnl]"(a"
stock,"ranging"from"0"to"1)."This"stock"serves"to"translate"the"values"of"‘Historically"largest"
niche"market’"[dmnl]"and"‘Duration"above"threshold’"[dmnl]"into"a"specific"value"that"can"be"
used"to"calculate"the"‘Sailing"ship"effect’"[dmnl]."We"do"so"as"follows:"If"the"‘Historically"
largest"niche"market’"[dmnl]"did"not"exceed"the"‘Size"threshold"SSE’"[dmnl],"the"‘Sailing"ship"
effect’"[dmnl]"is"calculated"with"the"‘Historically"largest"niche"market’"[dmnl]"(phase"A)."If"
the"size"threshold"has"been"passed,"we"need"to"determine"if"the"duration$threshold"has"
been"passed."Note"that"we"assumed"the"‘Sailing"ship"effect’"[dmnl]"to"be"highly"persistent,"
and"its"effect"is"not"likely"to"decline"before"the"duration"threshold"has"been"reached."As"
such,"if"the"duration"threshold"has"not"been"passed,"then"the"‘Sailing"ship"effect’"[dmnl]"is,"
calculated"by"means"of"the"‘Size"threshold"SSE’"[dmnl]."This"implies"the"highest"possible"
effect"size"(phase"B)."If"the"‘Duration"threshold"SSE’"[month]"has"been"exceeded,"then"the"
‘Sailing"ship"effect’"[dmnl]"is,"once"more,"determined"by"the"‘Historically"largest"niche"
market’"[dmnl];"following"Figure"5,"this"implies"a"potential"decline"of"the"‘Sailing"ship"effect’"
[dmnl]"(phase"C)."Figure"4"outlines"the"reasoning"behind"Equation"28."
"
Figure&4.&Reasoning&behind&Equation&28."
!"#$%#&'()*+,&-.+/#$$0)
$#.1',&)2+/3')4#.5'&)6)7+8')
&3.',3-$9)77!
:!7);<%+$9=%>)>3#,')-?)&3')
7#+$+21),3+>)'??'/&=>3#,')@AB)
Historically+largest+niche+
market
CD);7+8')&3.',3-$9)3#,)E''2)
.'#/3'9AB)!"#$%#&'()
Duration+above+threshold+<+
Duration+threshold+SSE
:!7);7#+$+21),3+>)'??'/&)
.'4#+2,)#&)4#F+4%4)$'"'$)
%2&+$)9%.#&+-2)&3.',3-$9)3#,)
E''2)'F/''9'9=>3#,')<A()
Size+threshold+SSE
CD);G%.#&+-2)&3.',3-$9)
.'#/3'9H)9'/$+2')+2)7#+$+21)
,3+>)'??'/&)>-,,+E$'=>3#,')
IA()Historically+largest+niche+
market
-"18"-"
Given"that"this"effect"follows"from"the"response"of"incumbents"on"TIS"growth,"we"
model"the"delay"‘AT"SSEs’"[month]."This"results"in"Equation"28."
(28)$Change$in$SSE$status$[dmnl/month]:$
d$(SSE$status)$/$dt$=$IF$THEN$ELSE$($Historically$largest$niche$market$<$Size$threshold$SSE,$
Historically$largest$niche$market,$IF$THEN$ELSE$($Duration$above$threshold$<$Duration$
threshold$SSE,$Size$threshold$SSE,$Historically$largest$niche$market)$/$AT$SSEs$
"
Subsequently,"the"‘SSE"status’"[dmnl]"determines"the"variable"‘Sailing"ship"effect’"
[dmnl]."Given"the"non-linear"nature"of"this"relationship"(De"Liso"and"Filatrella,"2008),"we"
adopted"a"lookup"variable"‘Effect"SSEs"on"SSE’"(see"Figure"5)."
"
"
Figure&5.&Non-linear&relation&between&‘SSE&status’&and&the&‘Sailing&ship&effect’."
"
As"can"be"seen"in"Figure"5,"the"potential"maximum"‘Sailing"ship"effect’"[dmnl]"equals"
1."Following"Equation"25,"such"effect"size"would"result"in"a"‘Regime"resistance"toward"TIS’"of"
1"and"a"‘Perceived"legitimacy"of"the"TIS’"of"0;"and"thus"guaranteed"TIS"failure."As"such,"we"
scale"the"‘Sailing"ship"effect’"(i.e.,"the"outcome"of"the"lookup"function"given"by"‘Effect"SSEs"
on"SSE’)"with"the"constant"‘Maximum"effect"size"SSE’"[Dmnl]—as"in"Equation"29."
(29)$Sailing$ship$effect$[dmnl]$=$Effect$SSEs$on$SSE$(SSE$status)$*$Maximum$effect$size$SSE$
"
The"Sailing"ship"effect"then"feeds"into"the"‘Regime"resistance"toward"TIS’"[dmnl]"
(Equation"25),"which"subsequently"determines"part"of"the"‘Perceived"legitimacy"of"the"TIS’"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.000
0.202
0.207
0.212
0.217
0.222
0.227
0.232
0.237
0.241
0.246
0.251
0.256
0.261
0.266
0.271
0.276
0.280
0.285
0.290
0.295
Sailing ship effect
SSE status
-"19"-"
[dmnl]"(Equation"9)."As"such,"this"concludes"the"description"of"the"balancing"‘Sailing"ship"
effect"loop’"(loop"B.6)."
EXOGENOUS&INPUTS&
The"model,"as"described"so"far,"is"fully"endogenous"in"nature."Yet,"as"noted"throughout"this"
text,"there"are"two"important"exogenous"inputs"that"influence"TIS"development."First"of"all,"
there"is"‘Landscape"pressure’"[dmnl],"which"lowers"the"‘Regime"resistance"toward"TIS’"
[dmnl]."Secondly,"the"model’s"dynamics"are"started"by"means"of"‘Fixed"external"resources’"
[Euro]."As"explained,"these"funds"can"feed"into"technology"development"as"well"as"the"
market"development"(through"‘External"resources’"[Euro],"Equation"13).""
In"an"attempt"to"keep"the"model"parsimonious,"we"describe"both"inputs"in"terms"of"
(a)"size"[dmnl"or"Euro],"(b)"timing"[month],"and"(c)"duration"[month]."Equation"30"details"the"
‘Landscape"pressure’"[dmnl];"and"Equation"31"details"the"‘Fixed"external"resources’"[Euro].""
(30)$Landscape$pressure$[dmnl]$=$IF$THEN$ELSE$(Time$>=$Timing$LP$:AND:$Time$<$Timing$LP$+$
Duration$LP,$Size$LP,$0)$
"
$(31)$Fixed$external$resources$[Euro]$=$IF$THEN$ELSE$(Time$>=$Timing$FER$:AND:$Time$<$
Timing$FER$+$Duration$FER,$Size$FER,$0)$
"
RANDOM&VARIATIONS&
As"outlined"in"the"manuscript,"we"included"sources"of"random"variation"to"the"model."More"
specifically"to"the"growth"and"decline"in"‘Technological"knowledge"developed’,"
‘Technological"knowledge"diffused’,"‘Entrepreneurial"activity’,"‘TIS"structures’,"and"‘Niche"
market’."We"modelled"this"by"means"of"so-called"‘Pink"noise’"[dmnl—%]"(Sterman,"2000)."
More"specifically,"the"following"stock"and"flow"structure"was"used—with"adjustment"time"
‘AT"noise’"[month]."
(32)$Change$in$Pink$noise$[dmnl—%]$
d$(Pink$noise)$/$dt$=$(1$+$Normal$distribution$–$Pink$noise)$/$AT$noise$
"
(33)$Normal$distribution$[dmnl]$=$RANDOM$NORMAL$(-5,$5,$0,$5,$Seed$x)$
"
-"20"-"
Five"different"‘seeds’"(see"Equation"33)"were"used"to"create"five"different"‘versions’"of"noise,"
each"version"influencing"one"or"more"flows."Table"1"detail"which"flow"was"subject"to"what"
‘version’"of"noise."""
"
Table&1.&Pink&noise&–&Flow&relationships.&
Pink&noise&‘version’&
Introduced&to&flow&
Pink"noise"1"
Knowledge"development"rate"(Equation"2);"Knowledge"loss"rate"
(Equation"4)"
Pink"noise"2"
Knowledge"decay"rate"(Equation"1);"Knowledge"diffusion"rate"
(Equation"5)"
Pink"noise"3"
Entrepreneurial"interest"rate"(Equation"10)"
Pink"noise"4"
Change"in"niche"market"(Equation"18)"
Pink"noise"5"
Entrepreneurial"disinterest"rate"(Equation"12);"Change"in"FIS"
(Equation"18)"
"
We"multiplied"the"‘Pink"noise’"[dmnl—%]"with"the"numerator"of"the"targeted"flow."The"
following"adjustments"were"made"to"Equations"1,"2,"4,"5,"10,"12,"16,"and"18—resulting"in"
Equations"1a,"2a,"4a,"5a,"10a,"12a,"16a,"and"18a."We"present"the"new"functions"below."For"
the"reader’s"convenience,"first"the"original"function"is"given,"after"which"the"adjusted"
equation"is"presented."
(1)$Knowledge$decay$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$–$Technological$$knowledge$developed$/$
Knowledge$decay$time$[+$Knowledge$development$rate]$
"(1a)$Knowledge$decay$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$–$(Technological$knowledge$developed$*$Pink$
noise$2)$/$Knowledge$decay$time$[+$Knowledge$development$rate]$
"
(2)$Knowledge$development$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$+$((1$-$Technological$knowledge$developed)$*$
(Resources$to$R&D$*$Euro$to$knowledge$development$rate))$/$AT$TKDe$[–$Knowledge$decay$
rate]$
-"21"-"
(2a)$Knowledge$development$rate$[dmnl/month]:$
d$(Technological$knowledge$developed)$/$dt$=$+$((1-Technological$knowledge$developed)$*$
Pink$noise$1$*$(Resources$to$R&D$*$Euro$to$knowledge$development$rate))$/$AT$TKDe$[–$
Knowledge$decay$rate]$
"
(4)$Knowledge$loss$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$–$(Technological$knowledge$diffused$/$
Knowledge$decay$time)$–$(Technological$knowledge$diffused$*$(Knowledge$development$rate$
/$Technological$knowledge$developed))$[+$Knowledge$diffusion$rate]$
(4a)$Knowledge$loss$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$–$(Technological$knowledge$diffused$/$
Knowledge$decay$time)$–$(Technological$knowledge$diffused$*$(Knowledge$development$rate$
*$Pink$noise$1$/$Technological$knowledge$developed$))$[+$Knowledge$diffusion$rate]$
"
(5)$Knowledge$diffusion$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$+$((1$–$Technological$knowledge$diffused)$*$
(Resources$to$knowledge$diffusion$*$Euro$to$knowledge$diffusion$rate))$/$AT$TKDi$[–$
Knowledge$loss$rate]$
(5a)$Knowledge$diffusion$rate$[dmnl/month]:$
d$(Technological$knowledge$diffused)$/$dt$=$+$((1$–$Technological$knowledge$diffused)$*$(Pink$
noise$2$*$Resources$to$knowledge$diffusion$*$Euro$to$knowledge$diffusion$rate))$/$AT$TKDi$[–$
Knowledge$loss$rate]$
"
(10)$Entrepreneurial$interest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$+$((1$–$Entrepreneurial$activity)$*$(Effect$of$PLT$on$
EA(Perceived$legitimacy$of$the$TIS$+$Effect$funding$on$PLT))$/$AT$EI$[–$Entrepreneurial$
disinterest$rate]$
(10a)$Entrepreneurial$interest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$+$((1$-$Entrepreneurial$activity)$*$Pink$noise$3$*$Effect$of$PLT$
on$EA(Perceived$legitimacy$of$the$TIS$+$Effect$funding$on$PLT))$/$AT$EI$[–$Entrepreneurial$
disinterest$rate]"
-"22"-"
(12)$Entrepreneurial$disinterest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$–$Entrepreneurial$activity$/$AT$EDI$[+$Entrepreneurial$
disinterest$rate]$
(12a)$Entrepreneurial$disinterest$rate$[dmnl/month]:$
d$(Entrepreneurial$activity)$/$dt$=$–$Entrepreneurial$activity$*$Pink$noise$5$/$AT$EDI$[+$
Entrepreneurial$disinterest$rate]$
"
(16)$Change$in$TIS$structures$[dmnl/month]:$
d$(TIS$structures)$/$dt$=$(1$–$TIS$structures)$*$((Effect$of$EA$on$TISS(Entrepreneurial$activity)$+$
Effect$funding$on$TISS)$–$TIS$structures)$/$AT$TISS$
(16a)$Change$in$TIS$structures$[dmnl/month]:$
d$(TIS$structures)$/$dt$=$(1$–$TIS$structures)$*$Pink$noise$5$*$((Effect$of$EA$on$
TISS(Entrepreneurial$activity)$+$Effect$funding$on$TISS)$–$TIS$structures$)$/$AT$TISS$
"
(18)$Change$in$Niche$market$[dmnl/month]:$
d$(Niche$market)$/$dt$=$((Entrepreneurial$activity$*$TIS$structures)$–$Niche$market)$/$AT$NM$
(18a)$Change$in$Niche$market$[dmnl/month]:$
d$(Niche$market)$/$dt$=$(MIN$(Entrepreneurial$activity$*$TIS$structures$*$Pink$noise$4,$1)$–$
Niche$market)$/$AT$NM$
"
Due"to"the"‘Pink"noise’"[dmnl]"introduced"in"Equation"18a,"the"stock"‘Niche"market’"[dmnl]"
can"grow"larger"than"1"(which"should,"theoretically,"not"be"possible)."As"such,"a"‘MIN’"
statement"is"introduced"to"prevent"the"stock"from"growing"larger"than"1."""
"
EXPERIMENTAL&SETUP&
In"order"to"conduct"the"experiments"as"outlined"in"the"manuscript,"the"following"constants"
were"adjusted"(Note"that"all"the"constants"[incl."units"and"values]"are"listed"in"the"section"
‘Constants"and"initial"values’.):"
(a) ‘Landscape"pressure’"[dmnl]"was"the"same"(in"terms"of"size,"timing,"duration)"for"
every"experiment."
-"23"-"
(b) The"‘Fixed"external"resources’"[Euro]"varied"among"the"different"experiments"in"
terms"of:"
1. Timing:"a"proactive"resource"condition"(i.e.,"‘Fixed"external"resources’"[Euro]"
introduced"before"‘Landscape"pressure’"[dmnl])"versus"a"reactive"resource"
condition"(i.e.,"‘Fixed"external"resources’"[Euro]"introduced"at"the"same"time"
as"‘Landscape"pressure’"[dmnl)."
2. Duration:"Vary"between"10"and"15"years"of"‘External"resources’"(while"
keeping"the"‘size’"the"same).""
(c) We"varied"the"‘Regime-TIS"relation’"by"manipulating:"
1. The"‘Duration"threshold"SSE’"[month]"(shorter"for"a"‘Symbiotic’"relationship"
versus"longer"for"a"‘Competitive’"relationship)."
2. The"‘Maximum"effect"size"SSE’"[dmnl]"(lower"for"a"‘Symbiotic’"relationship"
versus"higher"for"a"‘Competitive’"relationship)."
(d) Finally,"we"modelled"three"resource"conditions"through"adjustment"of"the"constant"
‘External"resources"distribution’"[dmnl—%]:"
1. Technology-oriented"resource"conditions."
2. Market-oriented"resource"conditions."
3. Hybrid"conditions."
Table"2,"as"also"presented"in"the"manuscript,"provides"an"overview"of"all"conducted"
experiments.&
&
Table&2.&Experimental&setup."
&
De-alignment&and&re-
alignment&
Reconfiguration&
Transformation&
Technological&
substitution&
Regime-TIS&relation"
Symbiotic"
Symbiotic"
Competitive"
Competitive"
TIS&developed&
before&landscape&
event?"
No"
Yes"
No"
Yes"
Technology-oriented&
resource&conditions&
Experiment"1a"
Experiment"4a"
Experiment"7a"
Experiment"10a"
&
Experiment"1b"
Experiment"4b"
Experiment"7b"
Experiment"10b"
Market-oriented&
resource&conditions&
Experiment"2a"
Experiment"5a"
Experiment"8a"
Experiment"11a"
&
Experiment"2b"
Experiment"5b""
Experiment"8b"
Experiment"11b"
Hybrid&conditions&
Experiment"3a"
Experiment"6a"
Experiment"9a"
Experiment"12a"
&
Experiment"3b"
Experiment"6b"
Experiment"9b"
Experiment"12b"
-"24"-"
CONSTANTS&AND&INITIAL&VALUES&
Table"3"lists"all"the"constants"(incl."values"and"units)."Table"4"gives"all"the"initial"values"(incl."
values"and"units)."
"
Table&3.&List&of&all&the&constants&used."
Name&of&constant&
Value&
Unit&
Remark&
AT"EI"
12"
Month"
"
AT"TISS"
60"
Month"
"
AT"GoS"
3"
Month"
"
AT"NM"
24"
Month"
"
AT"noise"
6"
Month"
"
AT"PLT"
12"
Month"
"
AT"RM"
6"
Month"
"
AT"RRT"
12"
Month"
"
AT"SSEs"
12"
Month"
"
AT"TKDe"
3"
Month""
"
AT"TKDi"
3"
Month""
"
Duration"FER"
180"OR"240"
Month"
Experiments"a"versus"experiments"b"(see"
Table"2)"
Duration"LP"
60"
Month"
"
Duration"threshold"SSE"
12"OR"180"
Month"
Symbiotic"OR"Competitive"
Effect"size"FIS"on"RRT"
0.4"
Dmnl—%"
"
Effectiveness"and"efficiency"
factor"
0.25"
Dmnl—%"
"
Euro"to"change"in"TISS"
1/50.000"
Euro"/"
dmnl"
"
Euro"to"change"in"PLT"
1/15.000"
Euro"/"
Dmnl"
"
Euro"to"knowledge"
development"rate"
1/10.000"
Dmnl"/"
Euro"
"
Euro"to"knowledge"diffusion"
rate"
1/1.000"
Dmnl"/"
Euro"
"
External"resources"distribution"
0.75"OR"0.25"OR"
‘hybrid’1"
Dmnl—%"
Technology"push"OR"Market"pull"OR"Hybrid."
See"footnote.""
Knowledge"decay"time"
60"
Month""
"
Knowledge"resource"
distribution"
0.8"
Dmnl—%"
"
Market"resource"distribution"
(External"resources)"
0.5"
Dmnl—%"
"
Market"resource"distribution"
(Niche)"
0.1"
Dmnl—%"
"
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
"
1"The"hybrid"development,"as"outlined"in"the"manuscript,"goes"from"0.9"to"0.1"over"a"period"
of"36"months"(after"36"month,"it"remains"0.1"until"the"‘Duration"FER’"has"been"reached—as"
determined"by"Equation"31)."This"was"modelled"as"follows:"
$
IF$THEN$ELSE$(Time$>$Timing$FER$:AND:$Time$<$Timing$FER$+$36,$0.9$–$(0.8$/$36)$*$
(Time$–$Timing$FER),$IF$THEN$ELSE$(Time$<=$Timing$FER,$0.9,$0.1))$
-"25"-"
Name&of&constant&
Value&
Unit&
Remark&
Maximum"effect"size"SSE"
0.05"OR"0.25"
Dmnl"
Symbiotic"OR"Competitive"
Niche"input"distribution"
0.05"
Dmnl—%"
"
Niche"to"Euro"factor"
175.000"
Euro"/"
dmnl"
"
Seed"1"
3425"
Dmnl"
"
Seed"2"
11"
Dmnl""
"
Seed"3"
4312"
Dmnl""
"
Seed"4"
12355"
Dmnl""
"
Seed"5"
424"
Dmnl"
"
Size"FER"
3.600.000"
Euro"
This"number"can"be"scaled"if"also"the"four"
‘Euro"to"…’"constants"are"adjusted."
Size"LP"
0.15"
Dmnl"
"
Size"threshold"SSE"
0.05"OR"0.25"
Dmnl"
Symbiotic"OR"Competitive"
Timing"FER"
60"
Month"
"
Timing"LP"
60"OR"120"
"
Reactive"OR"Proactive"strategy"
Variable"input"percentage"
0.25"
Dmnl—%"
"
&
Table&4.&List&of&all&the&stock&and&initial&values&used."
Name&of&stock&
Initial&value&
Unit&
Technological"knowledge"developed"
0.01"
Dmnl"
Technological"knowledge"diffused"
0.01"
Dmnl"
Guidance"of"the"Search"
0"
Euro"
Perceived"legitimacy"of"the"TIS"
0"
Dmnl"
Entrepreneurial"activity"
0"
Dmnl"
Niche"market"
0"
Dmnl"
Regime"resistance"toward"TIS"
1"
Dmnl"
SSE"status"
0"
Dmnl"
Historically"largest"niche"market"
0"
Dmnl"
Duration"above"threshold"
0"
Dmnl"
Resource"mobilization"
0"
Euro"
Pink"noise"1"
1"
Dmnl—%"
Pink"noise"2"
1"
Dmnl—%"
Pink"noise"3"
1"
Dmnl—%"
Pink"noise"4"
1"
Dmnl—%"
Pink"noise"5"
1"
Dmnl—%"
"
CALIBRATION&AND&ROBUSTNESS&TESTS&
As"explained"in"the"manuscript,"we"devised"a"context"where"knowledge"diffusion"requires"
the"least"amount"of"resources;"followed"by"knowledge"development;"followed"by"the"
development"of"entrepreneurial"activity"and,"finally,"the"development"of"TIS"structures."
Following"Table"3,"this"implies"1/1.000"[dmnl/Euro];"1/10.000"[dmnl/Euro];"1/15.000"
[dmnl/Euro];"and"1/50.000"[dmnl/Euro]"respectively."In"this"respect,"we"modelled"a"certain"
(fixed)"resource"requirement"per"loop,"or"‘relative"resistance’—relative"to"its"state"(i.e.,"the"
higher"the"value"of"the"stock"in"question,"the"more"resources"are"required"to"sustain"that"
-"26"-"
state)."For"calibration"purposes,"the"relative"resistance"of"the"different"loops"(motors)"needs"
to"be"aligned"and"matched"to"the"context"under"investigation."In"the"manuscript,"the"
modelled"context"is"loosely"based"on"the"empirical"observations"that,"in"particular"for"
radical"innovations,"costs"increase"substantially"when"moving"from"invention"to"innovation"
and"deployment,"because"new"infrastructures"and"institutions"need"to"be"developed"(and,"
hence,"technology"development"is"significantly"easier"to"achieve"than"market"development)."
Furthermore,"loop"resistance"needs"to"be"aligned"with"resource"input"from"(a)"‘Fixed"
external"resources’"[Euro]"and"(b)"‘Niche"input’"[Euro]"(the"latter"being"determined"by"the"
‘Niche"to"Euro"factor’"[Euro/dmnl])."The"‘Fixed"external"resources’"should"be"set"in"such"a"
manner"that"TIS"development"starts."The"‘Niche"to"Euro"factor’"should"be"modelled"in"such"a"
manner"that"the"‘Market"motor"loop’,"once"dominant,"can"drive"the"system"(i.e.,"sufficient"
resources"should"originate"from"‘Niche"input’—in"relation"to"the"‘Euro"to"…’"constants)."The"
correct"value,"for"both"constants"(‘Niche"to"Euro"factor’"and"‘Niche"input’),"is"best"
determined"by"means"of"experimentation—while"carefully"considering"the"set"‘relative"
resistance’."(Furthermore,"the"resource"distribution"factors"might"also"need"adjustment"to"
suit"the"modelled"context/policies—see"the"pink"variables"in"Figure"1.)"
The"chosen"setup"(e.g.,"the"idea"of"relative"loop"resistance)"implies"that"many"
different"contexts"can"(rather"easily)"be"simulated"by"means"of"the"presented"model,"which"
we"hope"is"going"to"proof"beneficial"for"future"studies."
Extreme&conditions&tests&
The"model"should"behave"realistically,"even"under"extreme"conditions"(Sterman,"2000)."We"
subjected"the"model"to"extreme"conditions"by"setting"extreme"exogenous"inputs."More"
specifically,"the"two"main"exogenous"inputs"were"varied"between"extreme"low"and"extreme"
high"values."We"did"so"in"the"context"of"experiment"3b"(randomly"chosen)—while"keeping"
the"random"noise"constant"(‘Pink"noise’"stocks)."More"specifically,"the"model"was"run"with"a"
‘Fixed"external"resources’"[Euro]"of"0"and"40.000"(base"scenario"is"20.000"Euro);"and"with"a"
‘Landscape"pressure’"[dmnl]"of"0"and"1"(base"scenario"is"0.15"percent"points"dmnl)."Figure"6"
and"7"illustrate"the"result"of"these"experiments"(of"course,"more"variables,"stocks,"and"flows"
were"assessed)—both"tests"indicate"model"robustness"as"all"results"remain"within"the"
theoretically"set"boundaries"(0"and"1).""
-"27"-"
"
Figure&6.&Extreme&conditions&test:&Perceived&legitimacy&of&the&TIS.&(FER"="‘Fixed"External"
Resources’."LP"="‘Landscape"pressure’.)"
&
Figure&7.&Extreme&conditions&test:&Niche&market."(FER"="‘Fixed"External"Resources’."LP"="
‘Landscape"pressure’.)&
Perceived legitimacy of the TIS
0.3
0.225
0.15
0.075
0
0 60 120 180 240 300 360 420 480 540 600
Time (Month)
Dmnl
Perceived legitimacy of the TIS : Extreme - FER 40000
Perceived legitimacy of the TIS : Extreme - FER 0
Perceived legitimacy of the TIS : Extreme - LP 0
Perceived legitimacy of the TIS : Extreme - LP 1
Niche market
0.9
0.675
0.45
0.225
0
0 60 120 180 240 300 360 420 480 540 600
Time (Month)
Dmnl
Niche market : Extreme - FER 40000
Niche market : Extreme - FER 0
Niche market : Extreme - LP 0
Niche market : Extreme - LP 1
-"28"-"
Sensitivity&analyses&
The"sensitivity"analyses"are"best"directed"toward"the"most"important"elements"of"the"
model."For"the"discussed"model,"this"implies"testing"of"the"‘Euro"to"…’"constants"(i.e.,"‘Euro"
to"knowledge"diffusion"rate’,"‘Euro"to"knowledge"development"rate’,"‘Euro"to"change"in"PLT’,"
‘Euro"to"change"in"TISS’)."As"such,"we"varied"these"constants"randomly"(-5%"/"+5%)"over"250"
experiments"each"(i.e.,"univariate"tests)"(once"more,"in"the"context"of"experiment"3b—while"
keeping"the"random"noise"constant)."Figure"8,"9,"10,"and"11"show"the"results"(for"the"stock"
‘Niche"market’)."
"
"
Figure&8.&Sensitivity&analysis:&Euro&to&knowledge&diffusion&rate—output:&Niche&market.&
"
Sensitivity Knowledge Diffusion
50% 75% 95% 100%
Niche market
0.4
0.3
0.2
0.1
00 150 300 450 600
Time (Month)
-"29"-"
"
Figure&9.&Sensitivity&analysis:&Euro&to&knowledge&development&rate—output:&Niche&
market.&
"
Figure&10.&Sensitivity&analysis:&Euro&to&change&in&PLT—output:&Niche&market.&
"
Sensitivity Knowledge Development
50% 75% 95% 100%
Niche market
0.5
0.375
0.25
0.125
00 150 300 450 600
Time (Month)
Sensitivity PLT
50% 75% 95% 100%
Niche market
0.9
0.675
0.45
0.225
00 150 300 450 600
Time (Month)
-"30"-"
"
Figure&11.&Sensitivity&analysis:&Euro&to&change&in&TISS—output:&Niche&market.&
What"becomes"apparent"from"these"results"is"that"the"model"can"be"considered"robust"as"
the"confidence"bounds"are"rather"narrow"for"all"experiments."More"specifically,"for"the"
technology"development"side"(Figures"8"and"9),"this"is"true"for"the"complete"model"run"(until"
t"="600);"for"the"market"development"side"(Figure"10"and"11),"the"model"can"be"considered"
robust"until"about"t"="400."(The"results"thus"indicate"that"the"higher"‘resistance’"loops"are"
also"more"sensitive.)"With"respect"to"the"latter,"the"rather"long"model"run"(600"months),"in"
combination"with"the"existence"of"a"‘tipping"point’,"makes"that"some"of"the"model"runs"
result"in"a"self-sustaining"niche,"while"other"model"runs"result"in"a"declining"niche."This"then"
also"explains"the"rather"large"confidence"bounds"in"Figure"10"and"11"at"t$="600,"which"is,"as"
such,"not"necessarily"the"result"of"an"overly"‘sensitive’"model."This"latter"can"also"be"seen"in"
Figure"12,"which"shows"the"result"illustrated"in"Figure"11"in"a"different"manner."More"
specifically,"rather"than"displaying"confidence"bounds"(as"in"Figure"11),"individual"traces"are"
shown"in"Figure"12."The"effect"of"the"tipping"point,"from"about"t"="400"is"clearly"visible.""
"
Sensitivity TISS
50% 75% 95% 100%
Niche market
0.8
0.6
0.4
0.2
00 150 300 450 600
Time (Month)
-"31"-"
"
Figure&12.&Sensitivity&analysis:&Euro&to&change&in&TISS—output:&Niche&market&(individual&
traces).&
"
REFERENCES&
Aldrich,"H.E.,"Fiol,"C.M."1994."Fools"rush"in?"The"institutional"context"of"industry"creation."
Acad."Manage."Rev."19,"645–670.""
Christensen,"C.M.,"1992."Exploring"the"Limits"of"the"Technology"S-Curve."Part"I:"Component"
Technologies."Prod."Oper."Manag."1,"334–357."
Christensen,"C.M.,"1992."Exploring"the"limits"of"the"technology"S-curve."Part"II:"Architectural"
technologies."Prod."Oper."Manag."1,"358–366."
De"Liso,"N.,"Filatrella,"G.,"2008."On"Technology"Competition:"A"Formal"Analysis"of"the"
“sailing-Ship"Effect.”"Econ."Innov."New"Technol."17,"593–610.""
Geels,"F.W.,"Schot,"J.,"2007."Typology"of"sociotechnical"transition"pathways."Res."Policy"36,"
399–417."
Geels,"F.W.,"2005."Processes"and"patterns"in"transitions"and"system"innovations:"Refining"
the"co-evolutionary"multi-level"perspective."Technol."Forecast."Soc."Change"72,"681–
696."
Gort,"M.,"Klepper,"S.,"1982."Time"paths"in"the"diffusion"of"product"innovations."Econ."J."92,"
630–653.""
Sensitivity TISS
Niche market
0.8
0.6
0.4
0.2
00 150 300 450 600
Time (Month)
-"32"-"
Holtz,"G.,"2011."Modelling"transitions:"An"appraisal"of"experiences"and"suggestions"for"
research."Environ."Innov."Soc."Transit."1,"167–186."
Schilling,"M.A.,"Esmundo,"M.,"2009."Technology"S-curves"in"renewable"energy"alternatives:"
Analysis"and"implications"for"industry"and"government."Energ."Policy"37,"1767–1781.""
Sterman,"J.D.,"2000."Business"Dynamics:"Systems"Thinking"and"Modeling"for"a"Complex"
World,"McGraw"Hill,"New"York."
Suurs,"R.A.A.,"2009."Motors"of"Sustainable"Innovation:"Toward"a"theory"on"the"dynamics"of"
technological"innovation"systems."Utrecht"University,"Utrecht."
"
