Allee effect in prey’s growth reduces the dynamical complexity in prey-predator model with generalist predator

Abstract

Prey-predator models with Allee effect have great importance in the context of ecology. Allee effect refers to a positive relationship between population density and per capita growth rate. Here we examine the influences of Allee effect in a prey-predator interaction model with a generalist predator. First we consider a prey-predator model with a generalist predator without the Allee effect which exhibits rich and complex dynamics like bistability, tristability along with local and global bifurcations such as cyclic bifurcations of limit cycle, homoclinic bifurcation, etc. Next, we investigate the same model with Allee effect in prey’s growth. This modified model exhibits simpler dynamics compared to the previous model. Though it undergoes local and global bifurcations as in the previous model, but tristability does not occur in this model. Also, increase of Allee parameter turns the system more structurally stable compared to prey-predator model with generalist predator only. Some of the results are supported numerically since the interior equilibrium points can not be obtained analytically.