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Stationary distribution and extinction of a three-species food chain stochastic model. (English) Zbl 1392.92080

Summary: In this paper, we investigate long-time behaviour of a stochastic three-species food chain model. By Markov semigroups theory, we prove that the densities of this model can converge to an invariant density or can converge weakly to a singular measure in \(L^1\) under appropriate conditions. Further, several sufficient conditions for the extinction of the three species were obtained. Finally, numerical simulations are carried out to illustrate our theoretical results.

MSC:

92D25 Population dynamics (general)
60K15 Markov renewal processes, semi-Markov processes
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