Bifurcation Analysis of Food Chain Dynamics with Intraspecific Competition in Middle Predators

The study of food chains and their dynamics is crucial in understanding ecological systems’ complex interactions. In particular, the impact of intraspecific competition within predator species remains relatively underexplored in the literature. This research aims to develop a mathematical model of a food chain that includes intraspecific competition in the middle predators. The model developed for this research includes three species: a prey, a middle predator, and a top predator. The Lotka-Volterra model was used to formulate the model equations, which were then analysed for stability using bifurcation theory. The results demonstrate that intraspecific competition of the middle predator plays a crucial role in the system’s stability. The analysis reveals that the system undergoes both transcritical and Hopf bifurcations, resulting in switching stability and limit cycle oscillations. Overall, this research highlights the importance of considering the impact of intraspecific competition in middle predators when studying food chains. The model developed for this research provides a valuable tool for further exploration of this topic and can be used to inform conservation efforts and management strategies in natural populations. By better understanding the dynamics of food chains and the role of intraspecific competition, we can gain valuable insights into ecological systems and make more informed decisions about their preservation and management.