Complex dynamics in a tritrophic food chain model with general functional response

Abstract

This paper investigates the rich dynamics in a tritrophic food chain mathematical model, consisting of three species: prey, intermediate predators, and top predators. It is assumed that alternative food are supplied to intermediate predators in addition to feeding on prey. We consider a general Holling type response function and analyze the model. The existence and stability of six possible equilibrium points are established. These equilibrium points describe the various dynamics that could take place in the food chain. Hopf bifurcation, limit cycle, doubling periods, chaotic attractors, boundary crisis are observed in the numerical computations. Our results reveal the rich and complex dynamics of the interactions in the food chain. Recommendations for Resource Managers. Our investigation brings the followings to the attention of management:. • Coexistence among predators and prey in the same environment is possible provided a good management of some factors (such as contacts between species, additional food supply, growth rate of species, etc). • The dynamics is complex and highly sensitive to the above factors. Strange or unpredictable behaviors could be observed. • The rate at which species are killed by a single predator (i.e., the functional responses) significantly affects the population sizes of all the species and the overall dynamics in the food chain.