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Strange Periodic Attractors in a Prey-Predator System with Infected Prey

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  • Frank Hilker
  • Horst Malchow
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    Abstract

    Strange periodic attractors with complicated, long-lasting transient dynamics are found in a prey-predator model with disease transmission in the prey. The model describes viral infection of a phytoplankton population and grazing by zooplankton. The analysis of the three-dimensional system of ordinary differential equations yields several semi-trivial stationary states, among them two saddle-foci, and the sudden (dis-)appearance of a continuum of degenerated nontrivial equilibria. Along this continuum line, the equilibria undergo a fold-Hopf (zero-pair) bifurcation (also called zip bifurcation). The continuum only exists in the bifurcation point of the saddle-foci. Especially interesting is the emergence of strange periodic attractors, stabilizing themselves after a repeated torus-like oscillation. This form of coexistence is related to persistent and permanent ecological communities and to bursting phenomena.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 13 (2006)
    Issue (Month): 3 ()
    Pages: 119-134

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    Handle: RePEc:taf:mpopst:v:13:y:2006:i:3:p:119-134

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    Related research

    Keywords: Fold-Hopf (zero-pair) bifurcation; permanence; predation; strange periodic attractor; viral plankton infection; zip bifurcation;

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    Cited by:
    1. Pedro de Mendonça, 2013. "Nonlinear Phenomena in a Growing Economy with Convex Adjustment Costs," EERI Research Paper Series EERI RP 2013/05, Economics and Econometrics Research Institute (EERI), Brussels.

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