A class of stochastic predator-prey models with predator-stage structure and rate-dependent Holling Ⅲ type functional re-sponses are developed.Firstly,the existence and uniqueness of global positive solutions for stochastic model are obtained.Secondly,the existence and uniqueness of the ergodic stationary distribution are studied by constructing a suitable Lyapunov function and using the ergodic theory of Has'Minskii.Next,by solving the corresponding three-dimensional Fokker-Planck equation,the exact expres-sion of the probability density function of the stochastic predator-prey model near the positive equilibrium point is derived.Finally,the rationality of the theoretical results is verified by numerical simulation.
stochastic predator-prey modelstationary distributionstage structureratio-dependentprobability density function
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