Mathematical Biosciences and Engineering, 2013, 10(3): 777-786. doi: 10.3934/mbe.2013.10.777.

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

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Equilibrium solutions for microscopic stochastic systems in population dynamics

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

The present paper deals with the problem of existence of equilibrium solutionsof equations describing the general population dynamics at the microscopic levelof modified Liouville equation (individually--based model) corresponding to a Markovjump process. We show the existence of factorized equilibrium solutions and discussuniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposedunder the assumption of periodic structures.
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Keywords Markow jump process; Population dynamics; microscopic models; integro-differential equations.

Citation: MirosŁaw Lachowicz, Tatiana Ryabukha. Equilibrium solutions for microscopic stochastic systems in population dynamics. Mathematical Biosciences and Engineering, 2013, 10(3): 777-786. doi: 10.3934/mbe.2013.10.777

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