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Invariant probabilities for systems in a random environment — With applications to the brusselator

✍ Scribed by Manfred Ehrhardt

Publisher
Springer
Year
1983
Tongue
English
Weight
585 KB
Volume
45
Category
Article
ISSN
1522-9602

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✦ Synopsis

In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system's dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.

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