Equilibrium solutions for microscopic stochastic systems in population dynamics | Zendy

Mirosław Lachowicz | Zendy; Tatiana V. Ryabukha | Zendy

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Equilibrium solutions for microscopic stochastic systems in population dynamics

Author(s) -

Mirosław Lachowicz,

Tatiana V. Ryabukha

Publication year - 2013

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2013.10.777

Subject(s) - uniqueness , dynamics (music) , mathematics , population , statistical physics , mathematical economics , mathematical analysis , physics , demography , sociology , acoustics

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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