Analysis of a stochastic logistic model with diffusion

•Stochastic Logistic model with diffusion and Lévy jumps is proposed.•Critical value between stability and extinction for species in each patch is obtained.•Critical value has a close relationship with Lévy jumps.•Numerical simulations are introduced to validate the results.

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.