Dynamical behavior of a one-prey two-predator model with random perturbations. (English) Zbl 1510.92169
Summary: The objective of this paper is to systematically study the qualitative properties of a stochastic one-prey two-predator model. We have derived sufficient conditions (parametric restrictions) for extinction of each species and at the same time we also notice that when one or two species go extinction, remaining species can be stable in time average under same parametric restrictions, i.e., extinction of one or two species ensures about the stability in mean of other species. Next, we have proved that the system admits a stationary distribution under some simple parametric conditions, which can be considered as a stability of the system in weak sense. Finally, we have proved that system is globally asymptotically stable.
MSC:
| 92D25 | Population dynamics (general) |
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
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