Stochastic predator-prey model with Leslie-Gower and Holling-type II schemes with regime switching

Abstract

A predator-prey model with Leslie-Gower and Holling-type II schemes with regime switching will be considered, that is, both white and color noises are taken into account. We firstly show that there exists a globally unique solution to the stochastic predator-prey model by use of the comparison theorem. Then, asymptotic properties of the system will be examined and the conditions under which the system is stochastically persistent will be given. Moreover, lastly, we analyze the optimal harvesting policy of the stochastic prey-predator model with Markovian switching.