Asymptotic properties of a stochastic \(n\)-species Gilpin-Ayala competitive model with Lévy jumps and Markovian switching. (English) Zbl 1440.92055
Summary: In this paper, a stochastic \(n\)-species Gilpin-Ayala competitive model with Lévy jumps and Markovian switching is proposed and studied. Some asymptotic properties are investigated and sufficient conditions for extinction, non-persistence in the mean and weak persistence are established. The threshold between extinction and weak persistence is obtained. The results illustrate that the asymptotic properties of the considered system have close relationships with Lévy jumps and the stationary distribution of the Markovian chain. Moreover, some simulation figures are presented to confirm our main results.
MSC:
| 92D25 | Population dynamics (general) |
| 34F05 | Ordinary differential equations and systems with randomness |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic Gilpin-Ayala competitive model; persistence; Lévy jumps; Markovian chain; extinctionReferences:
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