Dynamics of prey predator with Holling interactions and stochastic influences

The ecological interaction between prey and predator is modeled in general linear (or) function of prey density. The main advantages of such functional response are its simplicity, and well understood. The functional response should depend not only on the prey density but also on the predator density. In this paper a two species prey predator eco system having Holing type III functional response under stochastic influence is investigated. The analysis for the stability, local as well as global, of the model is performed by employing the techniques of Routh-Hurwitz and Lyapunov. Diffusive instability is also verified by perturbation technique and Routh-Hurwitz criteria. The fluctuations of the population and their stability around the equilibrium point influenced by the noise are computed. Numerical simulations illustrated, the theoretical analysis. (C) 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.