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The existence and uniqueness of a global positive solution is proven for thesystem of stochastic differential equations describing a nonautonomousstochastic density dependent predator-prey model with Holling-type IIfunctional response disturbed by white noise, centered and non-centered Poissonnoises. Sufficient conditions are obtained for stochastic ultimate boundedness,stochastic permanence, non-persistence in the mean, weak persistence in themean and extinction of a population densities in the considered stochasticpredator-prey model.

Long-time dynamics of a stochastic density dependent predator-prey model with Holling II functional response and jumps