Blowing-up of deterministic fixed points in stochastic population dynamics

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Abstract

We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. (C) 2007 Elsevier.Inc. All rights reserved.

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Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • population dynamics, stochastic, deterministic limit
Original languageEnglish
Pages (from-to)319-335
JournalMathematical Biosciences
Volume209
Issue number2
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes