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
Herausgeber: TAYLOR & FRANCIS INC
Journal: MATHEMATICAL POPULATION STUDIES
Volumen: 13
Ausgabe: 3
Startseite: 119
Seitenende: 134
Zusammenfassung: 
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.
Beschreibung: 
International Conference on Computational and Mathematical Population Dynamics, Trento, ITALY, JUN, 2004
ISSN: 08898480
DOI: 10.1080/08898480600788568

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