Permanence of a stochastic prey–predator model with a general functional response

Abstract

Different from the existing methods, a new method is introduced to analyze the stochastic permanence and extinction of a stochastic predator–prey model with a general functional response and the random factors acting on both the intrinsic growth rates and the intra-specific interaction rates. In particular, the existence of a stationary distribution and weak convergence to a boundary process are investigated as well. Some numerical simulations are performed to illustrate our theoretical results and to show that the stochastic noises play an essential role in determining the permanence and extinction. To be more specific, appropriate intensities of white noises may make the predator and prey population fluctuate around their deterministic steady-state values; but too large intensities of white noises may make the predator and/or prey population go to extinction.