Abstract
We study an eco-epidemic model with two trophic levels in which the dynamics are determined by predator-prey interactions as well as the vulnerability of the predator to a disease. Using the concept of generalized models we show that for certain classes of eco-epidemic models quasiperiodic and chaotic dynamics are generic and likely to occur. This result is based on the existence of bifurcations of higher codimension such as double Hopf bifurcations. We illustrate the emergence of chaotic behavior with one example system.
Highlights
Mathematical models are essential tools in order to understand the mechanisms responsible for persistence or extinction of species in natural systems
We find that the coupling of both models introducing a disease in the predator population leads to complex dynamics such as quasiperiodic and chaotic motion
As a result we show that chaos is generic and prevalent for certain classes of eco-epidemic models
Summary
Mathematical models are essential tools in order to understand the mechanisms responsible for persistence or extinction of species in natural systems. To study stabilizing or destabilizing effects bifurcation theory is often applied to find the parameter regions where the steady state for the ecological or epidemiological model is stable with respect to perturbations. These analyses are based on specific models describing the relevant processes in form of ordinary differential equations (ODEs). In this paper we use the concept of generalized model to study the impact of a disease of the predator on the dynamics of a predator-prey system To this end we couple a generalized ecological model with an epidemic one and study the stability properties of the steady state.
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