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Stochastic Gomatam model of interacting species: non-equilibrium fluctuation and stability. (English) Zbl 1062.92075

Summary: The object of the article is to study the stability behaviour of the stochastic version of the Gomatam model of interacting species. The reproductive and mortality factors of the prey and predator species, respectively, are perturbed by coloured noises due to the random environment. Using spectral density analysis, we show that this system exhibits large fluctuations for high amplitude random forces. When the intraspecific interaction coefficients tend to zero along a straight line, this system exhibits abnormally large fluctuations with increasing time with periodic background noise. We also obtain a relation between the real part of the eigenvalues of the interaction matrix in the deterministic environment and the stability of this system in the stochastic environment.

MSC:

92D40 Ecology
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