Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations

Volume 80 / 2008

Jens Christian Claussen Banach Center Publications 80 (2008), 17-31 MSC: Primary 91A22; Secondary 60J20, 92D50, 92D15. DOI: 10.4064/bc80-0-1

Abstract

Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit $N\to \infty$ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in $1/\,\sqrt[]{N}$. Consequences and relations to some previous approaches are outlined.

Authors

  • Jens Christian ClaussenInstitute of Theoretical Physics and Astrophysics
    Christian-Albrecht University Kiel
    Leibnizstr. 15
    24098 Kiel, Germany
    e-mail

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