Predator-prey interaction coupled by parasitic infection: Limit cycles and chaotic behavior
Several extensive studies have been carried out to document the ability of parasites to alter the behavior of infected hosts [1-3]. In this paper, we discuss the population dynamic consequences of parasite-induced changes in the behavior of the two interacting species in a predator-prey system, by means of the development and analysis of mathematical models. First, in order to investigate the dynamic consequences of the parasite-induced changes in the foraging ability of the predator population, a model is proposed for the predator-prey system in which only the predator population is invaded by a parasite. Thus, the predator population can be divided into two groups, namely the susceptible members and the infected ones. Analysis of the model is accomplished through a singular perturbation argument, whereby explicit conditions are derived which differentiate various dynamic behaviors and show the existence of limit cycles, explaining the oscillatory patterns often observed in field data. Parasite-induced changes in, the prey's susceptibility to predation can also be modelled by a system of nonlinear differential equations [4] in which the prey population is divided into two classes; the susceptible members and the infectives, while the entire predator population is assumed to be infected with the parasite. Finally, a numerical investigation is carried out on the full four-dimensional model in which both the prey and predator populations are divided each into an infected group and a susceptible one. Bifurcation diagram is constructed in order to identify the ranges of the system parametric values for which chaotic behavior can be expected. (C) 1999 Elsevier Science Ltd. All rights reserved.
parasitic infection limit cycles chaotic behavior predator-prey systems