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Blowing-up of deterministic fixed points in stochastic population dynamics

Natiello, Mario LU and Solari, Hernan G. (2007) In Mathematical Biosciences 209(2). p.319-335
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
population dynamics, stochastic, deterministic limit
in
Mathematical Biosciences
volume
209
issue
2
pages
319 - 335
publisher
Elsevier
external identifiers
  • wos:000250330600001
  • scopus:34548577224
ISSN
0025-5564
DOI
10.1016/j.mbs.2007.02.002
language
English
LU publication?
yes
id
efe4df5d-53f9-43b6-a216-791116a87246 (old id 653967)
date added to LUP
2007-12-18 12:36:54
date last changed
2017-03-14 13:42:25
@article{efe4df5d-53f9-43b6-a216-791116a87246,
  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.},
  author       = {Natiello, Mario and Solari, Hernan G.},
  issn         = {0025-5564},
  keyword      = {population dynamics,stochastic,deterministic limit},
  language     = {eng},
  number       = {2},
  pages        = {319--335},
  publisher    = {Elsevier},
  series       = {Mathematical Biosciences},
  title        = {Blowing-up of deterministic fixed points in stochastic population dynamics},
  url          = {http://dx.doi.org/10.1016/j.mbs.2007.02.002},
  volume       = {209},
  year         = {2007},
}