A Generalized Fokker-Planck Equation in the Case of the Volterra Model

J. Roerdink*, A. Weyland

*Corresponding author for this work

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Abstract

Zwanzig and Mori's projection-operator method is used in order to derive a generalized nonlinear Fokker Planck equation for one "relevant" species in the many species conservative Volterra model. The deterministic, autonomous, Markovian equations of motion, when averaged over a suitable ensemble of initial conditions in general give rise to a non-autonomous, non-Markovian stochastic process for the evolution of this relevant species. Moreover, this relevant species may show irreversible damping, although self-interaction terms are absent in the many species model.
Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalBulletin of mathematical biology
Volume43
DOIs
Publication statusPublished - 1981
Externally publishedYes

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