InterJournal Complex Systems, 131
Status: Accepted
Manuscript Number: [131]
Submission Date: 971020
Controlling chaos in systems of coupled maps with long-range interactions
Author(s): Michael Doebeli

Subject(s): CX.00, CX.19, CX.34

Category: Brief Article

Abstract:

We propose a simple method for controlling spatial chaos in an ecological model describing many local populations that are coupled by long--range dispersal. Control is achieved by making adjustments to the population sizes in a subset of the local populations. No detailed knowledge of the dynamic mechanisms underlying the chaotic population fluctuations is required. Every few generations, the populations in the censused subset of habitats are either decreased or increased by a fixed proportion of the current size. This reduces spatial chaos to regular cycles over a broad range of parameters. Similar results can be obtained with variants of the control technique. The models we use are of a very general nature, describing systems of coupled oscillators. The control of chaos in such systems has so far mostly been achieved in cases where coupling is restricted to nearest neighbours, and where chaos is controlled by perturbing system parameters according to a complicated scheme based on detailed knowledge about the system's dynamic behaviour. In contrast, our methods are very simple and consist of perturbing dynamic variables, which are generally amenable to measurement and manipulation. Therefore, our methods may prove useful in natural systems where underlying processes are imperfectly understood and long-range interactions are the norm.

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