Stochastic bifurcations, a necessary and sufficient condition for a stochastic Beddington-DeAngelis predator-prey model. (English) Zbl 1466.34051
Summary: The stochastic bifurcation phenomena are investigated from the perspective of dynamic bifurcation on a stochastic Beddington-DeAngelis predator-prey model. And a critical value of the stochastic model is considered, which shows the species \(x ( t )\) is persistent, however, the species \(y ( t )\) goes to extinction. Under certain conditions, a necessary and sufficient condition for persistence and extinction is obtained. The main conclusions are verified by examples and numerical simulations.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34F05 | Ordinary differential equations and systems with randomness |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34F10 | Bifurcation of solutions to ordinary differential equations involving randomness |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 92D25 | Population dynamics (general) |
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