A Chaotic System: Discretization and Control

  • Walter J. Grantham
  • Amit M. Athalye
Part of the Mathematical Modelling book series (MMO, volume 6)


This paper examines chaos in some population models for biological processes. In particular, the paper is concerned with chaos produced by discretization of continuous-time population models, and with the question of whether or not this chaotic behavior can occur when a feedback control management strategy is applied to continuous-time population models. Using two classical population models, it is shown that both exponential discretization and discretization associated with numerical simulation can produce chaos in the resulting discrete-time system. For example, a continuous-time Lotka-Volterra system exhibits periodic trajectories, but a particular discretization procedure is shown to yield discrete-time trajectories that all converge to a very complicated chaotic strange attractor, even if the discretization time steps are small. The results in the paper also show that this chaotic behavior can occur even if a feedback control management strategy is applied to the continuous-time system to stabilize the equilibrium point.


Equilibrium Point Chaotic System Feedback Controller Chaotic Motion Strange Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Birkhäuser Boston 1990

Authors and Affiliations

  • Walter J. Grantham
  • Amit M. Athalye

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