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Equilibrium solutions for microscopic stochastic systems in population dynamics

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


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