Bifurcation analysis and chaos control in discrete-time eco–epidemiological models of pelicans at risk in the Salton Sea

Abstract

Parasites play vital role in dynamics of predator–prey interaction and regulating bio-diversity. We study qualitative behavior of two 3-dimensional discrete-time predator–prey-parasite models. Bifurcation analysis and chaos control are discussed by taking into account the study of an eco–epidemiological model of pelicans at risk in the Salton Sea. Discrete-time models are obtained with implementations of Euler’s forward scheme and piecewise constant argument for differential equations. Local asymptotic stability of equilibria is investigated, and explicit Hopf bifurcation and period-doubling bifurcation criteria are implemented to discuss emergence of both type of bifurcations at positive steady-states of discrete-time models. Moreover, some chaos control techniques are implemented for controlling chaotic behavior under the influence of bifurcations. Numerical simulations are provided to illustrate theoretical discussion.