A Discrete-Time Modified Leslie-Gower Model with Double Allee Effect and Its Stability and Bifurcation Analysis

Abstract

Generally, all the models discussed so far are continuous time models. The continuous time models are quite apt at explaining the phenomena they are trying to predict and have known methods to get information from these type of models. But these models are not accurate for the physical systems which are observed over discreet time periods or which have non-continuous phenomena embedded in them, like production of new generation. Some species like salmon have non-overlapping generation characteristics since they have an annual spawning season and are born each year at a certain time. The discrete models are much more apt in describing the nature’s complex dynamics than the continuous models. A discrete-time modified Leslie-Gower system with double Allee effect is studied in this paper. The stability analysis of interior fixed points is performed. Using center manifold theorem it is shown that the system under consideration exhibits period-doubling and Neimark-Sacker bifurcations. The numerical simulations are provided to illustrate the consistency of the theoretical results.