Interactive consequence of prey refuge in a tri-trophic food chain model

Abstract

The present article appertains to a tri-trophic food chain model of the interacting population, including partial prey refuge and intra-specific competition among the predators. The precursory issues, including boundedness and dissipativeness of the system, are established. The stability analyses corresponding to the feasible equilibria of the present system are carried out systematically with special emphasis on global stability. The system appears to undergo Hopf-bifurcation depending on the appropriate set of model parameter values. In the absence of any intra-specific competition, the system exposes chaotic behaviour which is duly confirmed by Lyapunov exponents. On the contrary, such a chaotic response disappears for a specific value of self-interaction. Attention is also focused on the consequences of prey refuge graphically, which possesses a stabilizing effect and can control the system`s chaotic dynamics, leading to period-doubling and limit cycles. Finally, numerical simulations are performed for the purpose of model validation regarding its applicability in the realm of ecological food chain systems.