Supplement of Additional Food: Dynamics of Self-Competitive Prey–Predator System Incorporating Prey Refuge

Abstract

This paper deals with the dynamics of a prey-dependent two-species model, associating the Holling type II response function. We incorporate the prey refuge to the system with additional food supplement to self-competitive predator. We have found three ecologically significant equilibrium points as well as discussed their stability, instability conditions. The obtained results suggest that the coexisting equilibrium point can go through a Hopf bifurcation for some suitable value of prey refuge. Numerical simulations are performed to support all the analytical findings and to investigate the effects of additional food and self-interactions among predators for various densities of prey refuge. It can be observed that additional food supports coexisting behavior while intraspecific competition does not enhance coexistence so much but reducing the predator population, supports a stable solution. Although a very strong prey refuge forces the predators to extinct in both cases. Moreover, a comparison of four food web models has been performed to elaborate significantly the effects of prey refuge, additional food, and self-competition, respectively, on the system dynamics. The results yield that the model can fairly illustrate a realistic environmental ecology of two interacting populations and may be useful for species conservation.