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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. © 2007 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Blowing-up of deterministic fixed points in stochastic population dynamics
Autor:Natiello, M.A.; Solari, H.G.
Filiación:Center for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave: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
Año:2007
Volumen:209
Número:2
Página de inicio:319
Página de fin:335
DOI: http://dx.doi.org/10.1016/j.mbs.2007.02.002
Título revista:Mathematical Biosciences
Título revista abreviado:Math. Biosci.
ISSN:00255564
CODEN:MABIA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255564_v209_n2_p319_Natiello

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Citas:

---------- APA ----------
Natiello, M.A. & Solari, H.G. (2007) . Blowing-up of deterministic fixed points in stochastic population dynamics. Mathematical Biosciences, 209(2), 319-335.
http://dx.doi.org/10.1016/j.mbs.2007.02.002
---------- CHICAGO ----------
Natiello, M.A., Solari, H.G. "Blowing-up of deterministic fixed points in stochastic population dynamics" . Mathematical Biosciences 209, no. 2 (2007) : 319-335.
http://dx.doi.org/10.1016/j.mbs.2007.02.002
---------- MLA ----------
Natiello, M.A., Solari, H.G. "Blowing-up of deterministic fixed points in stochastic population dynamics" . Mathematical Biosciences, vol. 209, no. 2, 2007, pp. 319-335.
http://dx.doi.org/10.1016/j.mbs.2007.02.002
---------- VANCOUVER ----------
Natiello, M.A., Solari, H.G. Blowing-up of deterministic fixed points in stochastic population dynamics. Math. Biosci. 2007;209(2):319-335.
http://dx.doi.org/10.1016/j.mbs.2007.02.002