# Jens StarkeUniversity of Rostock · Institut für Mathematik

Jens Starke

Professor, Dr.rer.nat.

## About

94

Publications

9,606

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,003

Citations

Introduction

The focus of my work is on problems concerning dynamics (diff. equ., dyn. systems, stoch. many particle sys.) in modelling, analysis, numerics, simulation and optimization of complex scientific, medical and engineering systems. Besides mathematical theory, real-world applications of nonlinear mathematics are an important part of my work. My research contains in particular the interplay between discrete and continuous as well as deterministic and stochastic models and corresponding methods.

Additional affiliations

October 2016 - present

September 2015 - September 2016

April 2006 - August 2015

## Publications

Publications (94)

Computational modelling of deep brain stimulation for obsessive-compulsive disorder is vital for understanding the complex neural mechanisms underlying the disorder and for optimising treatment efficacy. This work presents a computational study investigating the intricate relationship between an advanced volume conductor model and a biophysical net...

The striatum as part of the basal ganglia is central to both motor, and cognitive functions. Here, we propose a large-scale biophysical network for this part of the brain, using modified Hodgkin-Huxley dynamics to model neurons, and a connectivity informed by a detailed human atlas. The model shows different spatio-temporal activity patterns corres...

Numerical continuation tools are nowadays standard to analyse nonlinear dynamical systems by numerical means. These powerful methods are unfortunately not available in real experiments without having access to an accurate mathematical model. Implementing such a concept in real world experiments using control and data processing to track unstable st...

A large-scale biophysical network model for the isolated striatal body is developed to optimise potential intrastriatal deep brain stimulation applied to, e.g. obsessive-compulsive disorder. The model is based on modified Hodgkin–Huxley equations with small-world connectivity, while the spatial information about the positions of the neurons is take...

In this study, we develop a large-scale biophysical network model for the isolated striatal body to optimise potential intrastriatal deep brain stimulation applied in, e.g. obsessive-compulsive disorder by using spatiotemporal patterns produced by the network. The model uses modified Hodgkin-Huxley models on small-world connectivity, while the spat...

A bstract
In this study, we develop a large-scale biophysical network model for the isolated striatal body to optimise potential intrastriatal deep brain stimulation applied in, e.g. obsessive-compulsive disorder by using spatiotemporal patterns produced by the network. The model uses modified Hodgkin-Huxley models on small-world connectivity, whil...

Numerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately, the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states whi...

Objective. Constructing a theoretical framework to improve deep brain stimulation (DBS) based on the neuronal spatiotemporal patterns of the stimulation-affected areas constitutes a primary target.
Approach. We develop a large-scale biophysical network, paired with a realistic volume conductor model, to estimate theoretically efficacious stimulatio...

Numerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states whic...

The motion of pedestrians is a paradigmatic phenomenon to study collective human behavior. We propose a model-free approach to analyze the movement of pedestrians in experiments and get a quantitative understanding of crowd dynamics. Using concepts from control and analysis of dynamical systems, we set up a scheme which allows us to identify dynami...

An important question in computational neuroscience is how to improve the efficacy of deep brain stimulation by extracting information from the underlying connectivity structure. Recent studies also highlight the relation of structural and functional connectivity in disorders such as Parkinson's disease. Exploiting the structural properties of the...

Non-pharmacological interventions (NPIs), principally social distancing, in combination with effective vaccines, aspire to develop a protective immunity shield against pandemics and particularly against the COVID-19 pandemic. In this study, an agent-based network model with small-world topology is employed to find optimal policies against pandemics...

This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the potential viability of the underlying feedback control techniques in an experiment. In contrast to previous e...

A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa...

Non-pharmacological interventions (NPIs), and in particular social distancing, in conjunction with the advent of effective vaccines at the end of 2020, aspired for the development of a protective immunity shield against the spread of SARS-CoV-2. The main question rose is related to the deployment strategy of the two doses with respect to the impose...

We address a biophysical network dynamical model to study how the modulation of dopamine (DA) activity and related N-methyl-d-aspartate (NMDA) glutamate receptor activity as well as the emerging Pre-Frontal Cortex (PFC) functional connectivity network (FCN) affect inhibitory cognitive function in schizophrenia in an antisaccade task. The values of...

Non-pharmacological interventions (NPIs), principally social distancing, in combination with effective vaccines, aspire to develop a protective immunity shield against pandemics and particularly against the COVID-19 pandemic. In this study, an agent-based network model with small-world topology is employed to find optimal policies against pandemics...

A large scale computational model of the basal ganglia (BG) network is proposed to describes movement disorder including deep brain stimulation (DBS). The model of this complex network considers four areas of the basal ganglia network: the subthalamic nucleus (STN) as target area of DBS, globus pallidus, both pars externa and pars interna (GPe-GPi)...

A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional coordinates into the high-dimensional phase space, then the high-dimensional (microscopic) evolution is applied for s...

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interacti...

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behav...

Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying the solution set of such noise contaminated zero probl...

Most learning processes in neuronal networks happen on a much longer time scale than that of the underlying neuronal dynamics. It is therefore useful to analyze slowly varying macroscopic order parameters to explore a network's learning ability. We study the synaptic learning process giving rise to map formation in the laminar nucleus of the barn o...

Severe accidents with many fatalities have oc-curred when too many pedestrians had to maneuver in too tight surroundings, as during evacuations of mass events. This demonstrates the importance of a better general understanding of pedestrians and emergent complex behavior in crowds. To this end, we develop both a new microscopic agent-based pedestri...

Equation-free methods make possible an analysis of the evolution of a few
coarse-grained or macroscopic quantities for a detailed and realistic model
with a large number of fine-grained or microscopic variables, even though no
equations are explicitly given on the macroscopic level. This will facilitate a
study of how the model behavior depends on...

Interacting particle systems constitute the dynamic model of choice in a variety of application areas. A prominent example is pedestrian dynamics, where good design of escape routes for large buildings and public areas can improve evacuation in emergency situations, avoiding exit blocking and the ensuing panic. Here we employ diffusion maps to stud...

The optimal-velocity follow-the-leader model is augmented with an equation that allows each driver to adjust their target headway according to the velocity difference between the driver and the car in front. In this more detailed model, which is investigated on a ring, stable and unstable multipulse or multijam solutions emerge. Analytical investig...

The possibility of controlling traffic dynamics by applying high-frequency time modulation of traffic flow parameters is studied. It is shown that the region of the car density where the uniform (free) flow is unstable
changes in the presence of time modulation compared with the unmodulated case. This region shrinks when the speed-up of cars does n...

We investigate a non-invasive, locally stabilizing control scheme
necessary for an experimental bifurcation analysis. Our test-rig
comprises a harmonically forced impact oscillator with hardening spring
nonlinearity controlled by electromagnetic actuators, and serves as a
prototype for electromagnetic bearings and other machinery with build-in
actu...

A piecewise-linear model with a single degree of freedom is derived from
first principles for a driven vertical cantilever beam with a localized mass
and symmetric stops. The resulting piecewise-linear dynamical system is
smoothed by a switching function (nonlinear homotopy). For the chosen smoothing
function it is shown that the smoothing can indu...

Several dynamical system approaches to combinatorial optimization problems
are described and compared. These include dynamical systems derived from
penalty methods; the approach of Hopfield and Tank; self-organizing maps, that
is, Kohonen networks; coupled selection equations; and hybrid methods. Many
of them are investigated analytically, and the...

A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage of heterogeneous performance of the drivers in time as we...

First, we give a rigorous convergence result for equation-free analysis in
the setting of slow-fast systems using implicit lifting. Second, we apply this
result to study the idealized traffic modeling problem of phantom jams
generated by cars with uniform behavior on a circular road. It is shown, that
the implicitly defined coarse-level time steppe...

In this paper we extend a method for iteratively improving slow manifolds so
that it also can be used to approximate the fiber directions. In its original
form the method was previously used succesfully by the first author and C.
Wulff to obtain slow manifolds, including normally elliptic ones in Hamiltonian
systems, with exponentially small error-...

The newly developed control-based continuation technique has made it possible to perform experimental bifurcation analysis, e.g. to track stable as well as unstable branches of frequency responses directly in experiments. The method bypasses mathematical models, and systematically explores how vibration characteristics of dynamical systems change u...

Using an equation-free analysis approach we identify a Hopf bifurcation point and perform a two-parameter continuation of the Hopf point for the macroscopic dynamical behavior of an interacting particle model. Due to the nature of systems with a moderate number of particles and noise, the quality of the available numerical information requires the...

The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when the re-laxation time is shorter than a critical one a spatially...

Self-organized modular approaches proved in nature to be robust and optimal and are a promising strategy to control future concepts of flexible and modular manufacturing processes. We show how this can be applied to a model of flexible manufacturing based on time-dependent robot-target assignment problems where robot teams have to serve manufacturi...

A coupling calculation method of dynamics and lubrication for rotor and floating bush bearing system has been developed to predict self-excited oscillations and unbalance oscillations using a flexible multibody dynamics technique with hydrodynamic lubrication theory. Based on experimental results of floating bush bearing, an accurate and numericall...

A coupling calculation method of dynamics and lubrication for rotor and floating bush bearing system has been developed to predict self-excited oscillations and unbalance oscillations using a flexible multibody dynamics technique with hydrodynamic lubrication theory. Based on experimental results of floating bush bearing, an accurate and numericall...

We consider a model class of interacting many-particle systems consisting of different types of particles defined by a gradient flow. The corresponding potential expresses attractive and repulsive interactions between particles of the same type and different types, respectively. The introduced system converges by self-organized pattern formation to...

A follow-the-leader model of traffic flow on a closed loop is considered in the framework of the extended optimal velocity (OV) model where the driver reacts to both the following and the preceding car. Periodic wave train solutions that describe the formation of traffic congestion patterns are found analytically. Their velocity and amplitude are d...

Mechanical systems are typically described with finite element models resulting in high-dimensional dynamical systems. The high-dimensional space excludes the application of certain investigation methods like numerical continuation and bifurcation analysis to investigate the dynamical behaviour and its parameter dependence. Nevertheless, the dynami...

We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary
differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our
approach is that it allows us to verify whether one can neglect gravitational forces after a cha...

Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum
single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the
macroscopic level is deterministic. It can be derived rigorously for low-pressure conditions from the...

In this paper we focus on methods for a reliable and robust
mechanism to distribute roles among a team of cooperating robots. In
previous work, we showed the principal applicability of a novel
approach based on self organization using coupled selection
equations. To show the applicability in the robocup scenario we used
a simple scenario to assign...

We focus on the reduction of the vibration level of rotors by optimizing the shape of the body. The target is to reduce rotor
weight and rotor vibrations leading to higher efficiency and less noise. We consider a finite element discretization of the
rotor using a Rayleigh beam model which includes rotary inertia and gyroscopic moments leading to no...

In the vertebrate brain external stimuli are often represented in distinct functional domains distributed across the cortical surface. Fast imaging techniques used to measure patterns of population activity record movies with many pixels and many frames, i.e., data sets with high dimensionality. Here we demonstrate that principal component analysis...

Spontaneous nucleation, pulse formation and propagation failure have been observed experimentally in CO oxidation on Pt(110) at intermediate pressures ( ≈ 10 − 2 mbar). This phenomenon can be reproduced with a stochastic model that includes temperature effects. Nucleation occurs randomly due to fluctuations in the reaction processes, whereas the su...

In this paper we focus on methods for a reliable and robust mechanism to distribute roles among a team of cooperating robots.
In previous work, we showed the principal applicability of a novel approach based on self organization using coupled selection
equations. To show the applicability in the robocup scenario we used a simple scenario to assign...

We present a mathematical model for calcium oscillations in the cilia of olfactory sensory neurons. The underlying mechanism is based on direct negative regulation of cyclic nucleotide-gated channels by calcium/calmodulin and does not require any autocatalysis such as calcium-induced calcium release. The model is in quantitative agreement with avai...

An analysis and visualization of craniofacial shape changes due to growth or orthodontic treatment is presented. The suggested method is based on an adapted Karhunen-Loève decomposition of time-discrete data based on landmarks in lateral X-rays of the skull. It allows for a reduction of the high-dimensional dynamic problem to a few spatial modes re...

The assignment of distributed mobile autonomous robots to targets, which occurs for instance as an important task in flexible manufacturing environments, is solved by using a self-organization approach motivated by pattern formation principles in biological, chemical, and physical systems. Similar to observations in many natural systems, such as an...

The assignment of distributed mobile autonomous robots to targets, which occurs for instance as an important task in flexible manufacturing environments, is solved by using a self-organization approach motivated by pattern formation principles in biological, chemical, and physical systems. Similar to observations in many natural systems, such as an...

In dynamic and complex multi-robot scenarios, the task assignment is
a challenging and crucial topic, because it has to be very exible
and robust or in some sense fault-tolerant to achieve a certain
degree of redundancy which is often required in these scenarios. To
cope with these requirements, a dynamic task assignment approach
based on selforgan...

Introduction In many medical or biological disciplines it is essential to understand and inuence the growth of organisms. Growth mechanisms comprise both a major change in size and a minor one in shape. The change in shape of the craniofacial skeletal structures is of particular clinical interest in dentofacial orthopedics and surgery. Many childre...

An approach based on Euclidean distances between cephalometric landmarks is presented (1) to visualize and localize the individual shape changes of the complex craniofacial skeleton during growth and (2) to depict the individual dynamic behavior of developmental size and shape changes.
Growth-related craniofacial changes were investigated exemplari...

The coupled selection equations were used for the dynamic control of the autonomous robots in RoboCup Scenario. This control method consisted of an algorithm based on pattern formation principles and a collision avoidance algorithm based on a behavioral force model. It was observed that they move according to the equation of motion using dynamic as...

Objective
An approach based on Euclidean distances between cephalometric landmarks is presented (1) to visualize and localize the individual shape changes of the complex craniofacial skeleton during growth and (2) to depict the individual dynamic behavior of developmental size and shape changes.
Patients and Method
Growth-related craniofacial chan...

Distributed autonomous robotic units are dynamically assigned to manufacturing targets in a model of a complex manufacturing environment such that an objective function like the total profit is optimized. The introduced control of the robotic units is based an a self-organization approach motivated by the selection of modes in pattern formation of...

We present a general model for the oxidation of CO on low-index platinum single crystal surfaces. In order to take fluctuations into account, it is first formulated in terms of stochastic birth–death processes. A corresponding deterministic limit for large particle numbers can be derived rigorously. The dynamical behavior of the reaction kinetics i...

Self-organized and error-resistant control of distributed
autonomous robotic units in a manufacturing environment with obstacles
where the robotic units have to be assigned to manufacturing targets in
a cost effective way, is achieved by using two fundamental principles of
nature. First, the selection behavior of modes is used which appears in
patt...