Pattern Formation in Intra-Specific Competition Food Chain System with Bifurcation and Chaos Control

Abstract

The study is an attempt to explore the competitive effects on the top predators in the tri-trophic food chain model. Holling types II and IV functional responses are used to investigate the complex behavior of the tri-trophic prey–predator system. Reaction–diffusion systems have been used to represent temporal evolution and spatial interaction among the species. Consequently, local and global stabilities, and Hopf-bifurcation have been analyzed. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions, signifying diffusion interaction between mid- and top-level predators. The effect of diffusion on the chaotic dynamics of the model systems is also investigated. It is found that the chaos mechanism wave-like behavior of the chaotic attractor exists for a long time. The diffusion of this long-term behavior is controlled by using Hybrid Control Strategy.