Dynamics of a three species ratio-dependent food chain model with intra-specific competition within the top predator

In this paper, a ratio-dependent food chain model has been considered. The total population has been divided into three classes, namely prey, predator and top-predator population. We have also incorporated intra-specific competition of predators in the model. We have studied the boundedness, dissipativeness and permanence of the solutions of the system and analyzed the existence of various equilibrium points and stability of the system at those equilibrium points. The system exhibits Bogdanov-Takens bifurcation, saddle-node bifurcation, Hopf bifurcation for suitable choice of the relevant parameters. The results of extensive numerical simulation are provided to support the validity of the theoretical findings. The ecological implications of our analytical and numerical findings are discussed.