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Time development of probability distributions for interacting species

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Abstract

A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.

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Authors and Affiliations

  1. Department of Physics, Drexel University, 19104, Philadelphia, Pennsylvania, USA

    Geral Rosen

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  1. Geral Rosen
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Rosen, G. Time development of probability distributions for interacting species. Bltn Mathcal Biology 41, 357–364 (1979). https://doi.org/10.1007/BF02460817

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  • DOI: https://doi.org/10.1007/BF02460817

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