Equilibrium solutions for microscopic stochastic systems in population dynamics

MirosŁaw Lachowicz; Tatiana Ryabukha

doi:10.3934/mbe.2013.10.777

Article Contents

2013, Volume 10, Issue 3: 777-786. Doi: 10.3934/mbe.2013.10.777

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Equilibrium solutions for microscopic stochastic systems in population dynamics

MirosŁaw Lachowicz^1, and
Tatiana Ryabukha^1,

1.
Institute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 Warsaw

Received: April 30, 2012

Revised: September 30, 2012

Published: March 2013

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Abstract

The present paper deals with the problem of existence of equilibrium solutions of equations describing the general population dynamics at the microscopic level of modified Liouville equation (individually--based model) corresponding to a Markov jump process. We show the existence of factorized equilibrium solutions and discuss uniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposed under the assumption of periodic structures.

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Mathematics Subject Classification: Primary: 92D25, 60J75, 45K05; Secondary: 35Q92, 35R09.

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