Blowing-up of deterministic fixed points in stochastic population dynamics

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, an...

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Autores principales: Natiello, Mario Alberto, Solari, Hernán Gustavo
Publicado: 2007
Materias:
Deterministic limit
Population dynamics
Stochastic
Eigenvalues and eigenfunctions
Lyapunov functions
Random processes
Stiffness matrix
System stability
Deterministic dynamics
Stochastic instability
eigenvalue
oscillation
population dynamics
stochasticity
article
nonhuman
population density
species extinction
statistical analysis
statistical model
stochastic model
Animals
Humans
Markov Chains
Mathematics
Models, Statistical
Population Dynamics
Stochastic Processes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255564_v209_n2_p319_Natiello
http://hdl.handle.net/20.500.12110/paper_00255564_v209_n2_p319_Natiello
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00255564_v209_n2_p319_Natiello
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spelling paper:paper_00255564_v209_n2_p319_Natiello2023-06-08T14:53:10Z Blowing-up of deterministic fixed points in stochastic population dynamics Natiello, Mario Alberto Solari, Hernán Gustavo Deterministic limit Population dynamics Stochastic Eigenvalues and eigenfunctions Lyapunov functions Random processes Stiffness matrix System stability Deterministic dynamics Deterministic limit Stochastic instability Population dynamics eigenvalue oscillation population dynamics stochasticity article nonhuman oscillation population density population dynamics species extinction statistical analysis statistical model stochastic model Animals Humans Markov Chains Mathematics Models, Statistical Population Dynamics Stochastic Processes 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. © 2007 Elsevier Inc. All rights reserved. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255564_v209_n2_p319_Natiello http://hdl.handle.net/20.500.12110/paper_00255564_v209_n2_p319_Natiello
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Deterministic limit
Population dynamics
Stochastic
Eigenvalues and eigenfunctions
Lyapunov functions
Random processes
Stiffness matrix
System stability
Deterministic dynamics
Deterministic limit
Stochastic instability
Population dynamics
eigenvalue
oscillation
population dynamics
stochasticity
article
nonhuman
oscillation
population density
population dynamics
species extinction
statistical analysis
statistical model
stochastic model
Animals
Humans
Markov Chains
Mathematics
Models, Statistical
Population Dynamics
Stochastic Processes
spellingShingle Deterministic limit
Population dynamics
Stochastic
Eigenvalues and eigenfunctions
Lyapunov functions
Random processes
Stiffness matrix
System stability
Deterministic dynamics
Deterministic limit
Stochastic instability
Population dynamics
eigenvalue
oscillation
population dynamics
stochasticity
article
nonhuman
oscillation
population density
population dynamics
species extinction
statistical analysis
statistical model
stochastic model
Animals
Humans
Markov Chains
Mathematics
Models, Statistical
Population Dynamics
Stochastic Processes
Natiello, Mario Alberto
Solari, Hernán Gustavo
Blowing-up of deterministic fixed points in stochastic population dynamics
topic_facet Deterministic limit
Population dynamics
Stochastic
Eigenvalues and eigenfunctions
Lyapunov functions
Random processes
Stiffness matrix
System stability
Deterministic dynamics
Deterministic limit
Stochastic instability
Population dynamics
eigenvalue
oscillation
population dynamics
stochasticity
article
nonhuman
oscillation
population density
population dynamics
species extinction
statistical analysis
statistical model
stochastic model
Animals
Humans
Markov Chains
Mathematics
Models, Statistical
Population Dynamics
Stochastic Processes
description 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. © 2007 Elsevier Inc. All rights reserved.
author Natiello, Mario Alberto
Solari, Hernán Gustavo
author_facet Natiello, Mario Alberto
Solari, Hernán Gustavo
author_sort Natiello, Mario Alberto
title Blowing-up of deterministic fixed points in stochastic population dynamics
title_short Blowing-up of deterministic fixed points in stochastic population dynamics
title_full Blowing-up of deterministic fixed points in stochastic population dynamics
title_fullStr Blowing-up of deterministic fixed points in stochastic population dynamics
title_full_unstemmed Blowing-up of deterministic fixed points in stochastic population dynamics
title_sort blowing-up of deterministic fixed points in stochastic population dynamics
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255564_v209_n2_p319_Natiello
http://hdl.handle.net/20.500.12110/paper_00255564_v209_n2_p319_Natiello
work_keys_str_mv AT natiellomarioalberto blowingupofdeterministicfixedpointsinstochasticpopulationdynamics
AT solarihernangustavo blowingupofdeterministicfixedpointsinstochasticpopulationdynamics
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