Dynamics of Complexity on Evolution of A Predator-Prey System Subject To Allee Effect on Prey Population

Abstract

The intricacy of the development of a discrete-time prey-predator system impacted by the Allee effect on the prey population has been thoroughly examined. The positive correlation between population density and overall individual fitness is known as the Allee effect, and it is a biological phenomenon. A discrete predator-prey system of the Lotka-Volterra type is the model taken into consideration in this work, assuming that interactions between two populations are non-overlapping generations. The system's fixed points were determined, and a thorough stability analysis of the fixed points was conducted. Both with and without the Allee effect, complex bifurcation patterns were seen in every instance.

In bifurcation diagrams, the emergence of several periodic windows within chaotic regions is also understood as showing multi-periodic orbits breaking into phenomena of chaos addition and period doubling, bi-stability, intermittency character, etc. These demonstrate that the system being examined is a complicated system. In order to determine regular and chaotic attractors, calculate Lyapunov exponents for regular and chaotic motions, and calculate topological entropies—which give the system's complexity—numerical simulation work was expanded. To determine the correlation dimensions of chaotic attractors, numerical computations were further expanded. Interesting images and a tabulated correlation dimension corroborate the study's findings. This study is important for bioscience and the issues surrounding harvesting phenomena in predator-prey relationships.