Chaotic Dynamics of a Simple Population Model under the Allee Effect

We look at the population dynamics of an ecological system considering the Allee effect across different levels of population growth rates. The model is described by the growth and degradation of population size by multiplying a threshold term by the Allee effect. When the population of a species is low, the population of the system is not maintained and collapses to extinction. A wide survival region is observed in the dynamics of the Allee effect, and we report a bifurcation diagram for selected control parameters. We identify the chaotic region based on Lyapunov exponents. We obtain a phase diagram distinguishing extinction, periodic oscillation, the chaotic region, and the unstable region in the control parameter space. We observe two sets of chaotic bands one for low and the other for high values of the Allee effect. The Allee effect diversifies the dynamic region in parameter space.