A remark on a stochastic logistic model with Lévy jumps. (English) Zbl 1328.34050
Summary: This note is concerned with a famous stochastic logistic equation with Lévy noises. Sufficient and necessary conditions for extinction and permanence are established. The results reveal that the Lévy noise may change the properties of population dynamics significantly. The results also reveal an important property of the Lévy noise: it is unfavorable for the permanence of the population. Some numerical simulations are introduced to validate the analytical results.
MSC:
| 34F05 | Ordinary differential equations and systems with randomness |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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