Wave of Chaos: New Mechanism of Pattern Formation in Spatio-temporal Population Dynamics

Authors: Petrovskii S.V.¹; Malchow H.²

Source: Theoretical Population Biology, Volume 59, Number 2, March 2001 , pp. 157-174(18)

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Abstract:

The dynamics of a simple prey–predator system is described by a system of two reaction- diffusion equations with biologically reasonable non-linearities (logistic growth of the prey, Holling type II functional response of the predator). We show that, when the local kinetics of the system is oscillatory, for a wide class of initial conditions the evolution of the system leads to the formation of a non-stationary irregular pattern corresponding to spatio-temporal chaos. The chaotic pattern first appears inside a sub-domain of the system. This sub-domain then steadily grows with time and, finally, the chaotic pattern invades the whole space, displacing the regular pattern. Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovsky Prospect 36, Moscow, 117218, Russia 2: Institute of Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabrück, Artilleriestrasse 34, Osnabrück, D-49069, Germany

Publication date: 2001-03-01