Allee Effect in Continuous-Time and Discrete-Time Predator-Prey Systems with Leslie Type

Abstract

In this presentation, we will discuss the Allee effect in continuous-time predator-prey system with Leslie type and its discrete version. First, the stability analysis of continuous system will be given. Then, we will examine the bifurcations and chaotic behavior of the model. Next, the impact of Allee effect on the dynamics of both prey and predator populations will be discussed via numerical simulations. Second, discrete-time predator-prey system obtained by applying the forward Euler scheme to its continuous-time counterpart will be introduced. Afterwards, the conditions on parameters for stability and periodic solutions will be stated briefly. Finally, some numerical simulations will be shown to compare the Allee effect in maintaining the intricate balance between predator and prey populations and the importance of considering complex ecological interactions in order to accurately model and understand the population dynamics in continuous (overlapping) and discrete (non-overlapping) cases.