Blowing-up of deterministic fixed points in stochastic population dynamics
(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:
https://lup.lub.lu.se/record/653967
- author
- Natiello, Mario LU and Solari, Hernan G.
- organization
- publishing date
- 2007
- 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
- 2016-04-01 16:18:55
- date last changed
- 2022-01-28 18:50:25
@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}},
keywords = {{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}},
doi = {{10.1016/j.mbs.2007.02.002}},
volume = {{209}},
year = {{2007}},
}