title: Equilibrium solutions for microscopic stochastic systems in population dynamics.
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.
authors.affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, 2, Banach Str., 02-097 Warsaw, Poland. lachowic@mimuw.edu.pl
authors.forename: Mirosław
authors.initials: M
authors.lastname: Lachowicz
authors.forename: Tatiana
authors.initials: T
authors.lastname: Ryabukha
mesh_terms: D000818:Animals; D005583:Fourier Analysis; D006801:Humans; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D009369:Neoplasms / Q000209:etiology / Q000473:pathology; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D013269:Stochastic Processes; D049490:Systems Biology