Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment.

• Existence of T-periodic solution for a stochastic Crowley-Martin model with impulse is investigated. • Asymptotical stability in probability for the Crowley-Martin model is discussed. • Existence and ergodicity of stationary distribution for the Markov switching case are studied. • Our conclusion improves and generalizes the corresponding existing ones. This paper systematically investigates a stochastic Crowley-Martin predator-prey model. Firstly, we derive sufficient conditions for the existence of positive T -periodic solution for the impulsive case. Secondly, distinguished from the previous papers, asymptotical stability in probability is investigated by combining Khasminskii theory of stability with Lyapunov method. Our conclusion also improves and extends the corresponding existing ones. Thirdly, we establish the sufficient criteria for the existence of a unique ergodic stationary distribution for the Markovian switching case. Finally, two numerical examples are presented to demonstrate the effectiveness and feasibility of our analytical results and reveal the respective effect of white noises and Markovian switching. [ABSTRACT FROM AUTHOR]