American Institute of Mathematical Sciences

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2009, 6(4): 855-871. doi: 10.3934/mbe.2009.6.855

Evidence of chaos in eco-epidemic models

Dirk Stiefs 1, , Ezio Venturino 2, and  Ulrike Feudel 3,

1. 

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
2. 

Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino
3. 

Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität Oldenburg, PF 2503, 26111 Oldenburg

Received  March 2009 Revised  May 2009 Published  September 2009

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.
Keywords: chaos, bifurcation., eco-epidemiology, generalized model.
Mathematics Subject Classification: Primary: 92D25, 92D30, 92D40; Secondary: 70K5.
Citation: Dirk Stiefs, Ezio Venturino, Ulrike Feudel. Evidence of chaos in eco-epidemic models. Mathematical Biosciences & Engineering, 2009, 6 (4) : 855-871. doi: 10.3934/mbe.2009.6.855
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