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Analysis of a stochastic logistic model with diffusion. (English) Zbl 1410.34172
Summary: Taking both white noise and Lévy jump noise into account, a stochastic logistic model with diffusion is proposed and considered. Under some simple assumptions, the almost complete parameters analysis of the model is carried out. In each case it is shown that the population in each patch is either stable in time average or extinct, depending on the parameters of the model, especially, depending on the intensity of the Lévy jump noise. Some simulation figures are introduced to validate the theoretical results.

MSC:
34F05 Ordinary differential equations and systems with randomness
92D25 Population dynamics (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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