Evidence of chaos in eco-epidemic models
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1.
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden
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2.
Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino
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3.
Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität Oldenburg, PF 2503, 26111 Oldenburg
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Received:
01 March 2009
Accepted:
29 June 2018
Published:
01 September 2009
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MSC :
Primary: 92D25, 92D30, 92D40; Secondary: 70K50.
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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.
Citation: Dirk Stiefs, Ezio Venturino, Ulrike Feudel. Evidence of chaos in eco-epidemic models[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 855-871. doi: 10.3934/mbe.2009.6.855
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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.
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