Multiplicative-noise Can Suppress Chaotic Oscillation in Lotka-Volterra Type Competitive Model

Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur - 208016, INDIA

^⋆ Corresponding author. E-mail: malayb@iitk.ac.in

Abstract

Recently, Wang and Xiao studied a four-dimensional competitive Lotka-Volterra system within a deterministic environment in [11]. With the help of numerical example they showed the existence of a chaotic attractor through the period doubling route. In this paper, we are interested to study the dynamics of the same model in presence of environmental driving forces. To incorporate the environmental driving force into the deterministic system, we perturb the growth rates of each species by white noise terms. Then we prove that the unique positive global solution exists for the noise added system and the general p-th order moment of it is bounded for p ≥ 1, which ensures that the solution is stochastically bounded. It is also shown that the solution of the stochastic system is stochastically permanent under some simple conditions. Finally , we demonstrate the noise induced oscillation for the concerned model with the help of numerical example..