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

Frank Hilker and Horst Malchow

Mathematical Population Studies, 2006, vol. 13, issue 3, 119-134

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.

Keywords: Fold-Hopf (zero-pair) bifurcation; permanence; predation; strange periodic attractor; viral plankton infection; zip bifurcation (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/08898480600788568

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