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

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  • Frank Hilker
  • Horst Malchow

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.

Suggested Citation

  • Frank Hilker & Horst Malchow, 2006. "Strange Periodic Attractors in a Prey-Predator System with Infected Prey," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(3), pages 119-134.
  • Handle: RePEc:taf:mpopst:v:13:y:2006:i:3:p:119-134
    DOI: 10.1080/08898480600788568
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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.
    2. repec:eee:ecomod:v:220:y:2009:i:7:p:931-939 is not listed on IDEAS

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