Stochastic prey-predator system with foraging arena scheme

In this paper, we extend the foraging arena model describing the dynamics of prey-predator abundance from a deterministic framework to a stochastic one. This is achieved by introducing the environmental noises into the growth rate of prey as well as the death rate of predator populations. We then prove that this stochastic differential equation (SDE) has a unique global positive solution. The long-time behaviours of the system are then developed. Furthermore the existence of a stationary distribution is pointed out under certain parametric restrictions. All the results are illustrated by the computer simulations.