InterJournal Complex Systems, 527
Status: Submitted
Manuscript Number: [527]
Submission Date: 20501
Revised On: 20629
Stability and oscillations in spatially-extended models of population interaction
Author(s): Nelli Ajabyan

Subject(s): CX.19, CX.08, CX.34

Category: Brief Article

Abstract:

This paper presents the investigation of oscillations and nonlinear dynamics of models of ecological systems with spatial heterogeneity. Orbit structure of a dynamical system is applied to stable structures definition in generalized models of population dynamics. It is so-called Lagrange stability that serves as a formal analogue of ecological stability defined in terms of conservation of species number in biological community. The dynamics of coupled oscillators is proved to be relevant in the study of pattern generation of a biological system. Patterns of Hopf bifurcation started with Turing model have been an active subject of research recent years [Medvinsky, 2000]]. Dynamics of nets of coupled oscillators is applied to definition of oscillations in spatially extended systems. Global bifurcation phenomena associated with networks of identical oscillators are reviewed. As an application global bifurcation of phase locked oscillators is applied to migratory effects investigation in spatially-discrete models of trophic chains.

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