Local bifurcations and chaos in a time-discrete food-chain model with strong pressure on preys [ Back ]

UAB - Dept. Matemàtiques (C1/-128)
Lluís Alsedà
Universitat Autònoma de Barcelona


Ecological systems are complex dynamical systems. Modelling efforts on the dynamical stability of ecosystems have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Experimental and field research has provided mounting evidence for the existence of chaotic fluctuations in species' abundances. Especially for discrete-time food chain systems. Discrete-time dynamics, mainly arising in temperate ecosystems for species with non-overlapping generations, have been largely studied to understand the dynamical outcome due to changes in relevant ecological parameters. The behaviour of many of these models is difficult to investigate in the parameter space, and most of these models have been studied mainly numerically when the dimension of the phase space is large. In this article we investigate a discrete-time food chain system considering two predators predating a single prey species. We provide a full description of the local behaviour of equilibria and stability within a volume of the parameter space containing relevant dynamics. The parameter space is build with three parameters including prey's growth rate and the predation rates. We discuss the behaviour of this model, paying special attention to the pressure of predators on the prey. The dynamics undergo the Ruelle-Takens-Newhouse route to chaos at increasing predation rates. Interestingly, we find that increasing predation directly on preys can shift the extinction of top predators to their survival, allowing an unstable persistence of the three species by means of periodic and strange chaotic attractors.