Open AccessEquilibrium 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.