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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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  • This article has been cited by:

    1. Mirosław Lachowicz, Andrea Quartarone, Tatiana V. Ryabukha, Stability of solutions of kinetic equations corresponding to the replicator dynamics, 2014, 7, 1937-5077, 109, 10.3934/krm.2014.7.109
    2. Marina Dolfin, Mirosław Lachowicz, Zuzanna Szymańska, 2014, Chapter 5, 978-1-4939-0457-0, 151, 10.1007/978-1-4939-0458-7_5
    3. Mirosław Lachowicz, A class of microscopic individual models corresponding to the macroscopic logistic growth, 2018, 41, 01704214, 8446, 10.1002/mma.4680
    4. Marina Dolfin, Mirosław Lachowicz, Modeling DNA thermal denaturation at the mesoscopic level, 2014, 19, 1553-524X, 2469, 10.3934/dcdsb.2014.19.2469
    5. Jacek Banasiak, Mirosław Lachowicz, 2014, Chapter 8, 978-3-319-05139-0, 223, 10.1007/978-3-319-05140-6_8
    6. João Miguel Oliveira, Maria Piedade Machado Ramos, Carolina Ribeiro, Ana Jacinta Soares, Equilibrium of a kinetic model of oscillating patterns for chronic autoimmune diseases, 2024, 0, 1937-5093, 0, 10.3934/krm.2024008
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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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