Stochastic non-autonomous Holling type-Ⅲ prey-predator model with predator's intra-specific competition

Abstract

The objective of this article is to study the significance of dynamical properties of non-autonomous deterministic as well as stochastic prey-predator model with Holling type-Ⅲ functional response. Firstly, uniform persistence of the deterministic model has been demonstrated. Secondly, stochastic non-autonomous prey-predator system with Holling type-Ⅲ functional response is proposed. The existence of a global positive solution has been derived. Sufficient conditions for non-persistence in mean, weakly persistence in mean, extinction have been derived. Moreover the sufficient conditions for permanence of the system have been established. The analytical results are verified by numerical simulation.