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A generalized Fokker-Planck equation in the case of the Volterra model

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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.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Nijmegen, The Netherlands

    J. Roerdink & A. Weyland

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  1. J. Roerdink
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  2. A. Weyland
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Roerdink, J., Weyland, A. A generalized Fokker-Planck equation in the case of the Volterra model. Bltn Mathcal Biology 43, 69–79 (1981). https://doi.org/10.1007/BF02460940

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  • DOI: https://doi.org/10.1007/BF02460940

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