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Qualitative theory of stochastic dynamical systems—Applications to life sciences

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Abstract

Qualitative theory for multidimensional stochastic dynamical models\(\dot x = f(x, \xi )\) is presented where the random influences ξ may be white or colored, i.e. a (possibly bounded) diffusion process. We concentrate on transience, stationary solutions and boundary behavior and discuss a set-up for reliable simulations. The method consists in associating a deterministic control system where the (approximate) controllability properties determine the qualitative behavior of the stochastic system. Applications to some biological systems indicate the usefulness of qualitative theory in life sciences.

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  1. Forschungsschwerpunkt “Dynamische Systeme”, University of Bremen, 2800, Bremen, West Germany

    Wolfgang Kliemann

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  1. Wolfgang Kliemann
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Kliemann, W. Qualitative theory of stochastic dynamical systems—Applications to life sciences. Bltn Mathcal Biology 45, 483–506 (1983). https://doi.org/10.1007/BF02459584

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