Blowing-up of deterministic fixed points in stochastic population dynamics
Författare
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Dynamical systems
Publiceringsår
2007
Språk
Engelska
Sidor
319-335
Publikation/Tidskrift/Serie
Mathematical Biosciences
Volym
209
Issue
2
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- population dynamics
- stochastic
- deterministic limit
Status
Published
Forskningsgrupp
- Analysis and Dynamics
- Dynamical systems
ISBN/ISSN/Övrigt
- ISSN: 0025-5564