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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 777-786. doi: 10.3934/mbe.2013.10.777
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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
  • Received: 01 May 2012 Accepted: 29 June 2018 Published: 01 April 2013

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

  • 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.

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

    Related Papers:

  • 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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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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