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

Abstract

The objective of this paper is to systematically investigate the dynamical properties of a ratio-dependent predator-prey system with Holling type IV functional response by white noise. The global existence of a positive unique solution to the system
with positive initial value is shown employing comparison theorem of stochastic equation and It^o's formula. We derived some appropriate conditions for the persistence in mean and extinction. This system has a stable stationary distribution and it is ergodic. Numerical simulations are carried out for further support of present research.