Fixed points stability, bifurcation analysis, and chaos control of a Lotka–Volterra model with two predators and their prey

Abstract

The study of the population dynamics of a three-species Lotka–Volterra model is crucial in gaining a deeper understanding of the delicate balance between prey and predator populations. This research takes a unique approach by exploring the stability of fixed points and the occurrence of Hopf bifurcation. By using the bifurcation theory, our study provides a comprehensive analysis of the conditions for the existence of Hopf bifurcation. This is validated through detailed numerical simulations and visual representations that demonstrate the potential for chaos in these systems. To mitigate this instability, we employ a hybrid control strategy that ensures the stability of the controlled model even in the presence of Hopf bifurcation. This research is not only significant in advancing the field of ecology but also has far-reaching practical implications for wildlife management and conservation efforts. Our results provide a deeper understanding of the complex dynamics of prey–predator interactions and have the potential to inform sustainable management practices and ensure the survival of these species.