Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

Abstract

In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predatorprey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and It??s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.