Weakly dissipative predator-prey systems

A. A. King, William M Schaffer, C. Gordon, J. Treat, M. Kot

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In the presence of seasonal forcing, predator-prey models with quadratic interaction terms and weak dissipation can exhibit infinite numbers of coexisting periodic attractors corresponding to cycles of different magnitude and frequency. These motions are best understood with reference to the conservative case, for which the degree of dissipation is, by definition, zero. Here one observes the familiar mix of 'regular' (neutrally stable orbits and tori) and chaotic motion typical of non-integrable Hamiltonian systems. Perturbing away from the conservative limit, the chaos becomes transitory. In addition, the invariant tori are destroyed and the neutrally stable periodic orbits becomes stable limit cycles, the basins of attraction of which are intertwined in a complicated fashion. As a result, stochastic perturbations can bounce the system from one basin to another with consequent changes in system behavior. Biologically, weak dissipation corresponds to the case in which predators are able to regulate the density of their prey well below carrying capacity.

Original languageEnglish (US)
Pages (from-to)835-859
Number of pages25
JournalBulletin of Mathematical Biology
Volume58
Issue number5
StatePublished - Sep 1996

Fingerprint

Predator prey systems
orbits
Dissipative Systems
Predator-prey System
Orbit
Dissipation
dissipation
Orbits
predator
basins
predators
Hamiltonians
Conservation of Natural Resources
carrying capacity
Chaos theory
Stochastic Perturbation
Bounce
Invariant Tori
Carrying Capacity
Chaotic Motion

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

King, A. A., Schaffer, W. M., Gordon, C., Treat, J., & Kot, M. (1996). Weakly dissipative predator-prey systems. Bulletin of Mathematical Biology, 58(5), 835-859.

Weakly dissipative predator-prey systems. / King, A. A.; Schaffer, William M; Gordon, C.; Treat, J.; Kot, M.

In: Bulletin of Mathematical Biology, Vol. 58, No. 5, 09.1996, p. 835-859.

Research output: Contribution to journalArticle

King, AA, Schaffer, WM, Gordon, C, Treat, J & Kot, M 1996, 'Weakly dissipative predator-prey systems', Bulletin of Mathematical Biology, vol. 58, no. 5, pp. 835-859.
King AA, Schaffer WM, Gordon C, Treat J, Kot M. Weakly dissipative predator-prey systems. Bulletin of Mathematical Biology. 1996 Sep;58(5):835-859.
King, A. A. ; Schaffer, William M ; Gordon, C. ; Treat, J. ; Kot, M. / Weakly dissipative predator-prey systems. In: Bulletin of Mathematical Biology. 1996 ; Vol. 58, No. 5. pp. 835-859.
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