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Simple Mathematical Models With Very Complicated Dynamics

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Robert M May at University of Oxford
Robert M May
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Abstract

First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.
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© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
© Nature Publishing Group1976
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... In this case, u = 3 (period 3) and i = r, indicating that X (r) , after three iterations, returns to itself. Additional superstable curves are highlighted in Fig. 2(a), labeled as [2] [4] r , and [4] m . It is noteworthy that all these curves are within a periodic region with high negative values of λ. ...
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