Strange periodic attractors in a prey-predator system with infected prey

Autor(en): Hilker, Frank M.
Malchow, Horst 
Stichwörter: COMPETITIVE COEXISTENCE; Demography; DISEASE; fold-Hopf (zero-pair) bifurcation; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; permanence; PHYTOPLANKTON; predation; PRINCIPLE; Social Sciences, Mathematical Methods; Statistics & Probability; strange periodic attractor; TRANSMISSION; viral plankton infection; VIRUSES; zip bifurcation
Erscheinungsdatum: 2006
Volumen: 13
Ausgabe: 3
Startseite: 119
Seitenende: 134
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.
International Conference on Computational and Mathematical Population Dynamics, Trento, ITALY, JUN, 2004
ISSN: 08898480
DOI: 10.1080/08898480600788568

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