caa a22 4500 477067611 CHVBK 20180405111417.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF02459486 doi (NATIONALLICENCE)springer-10.1007/BF02459486 Weakly dissipative predator-prey systems [Elektronische Daten] [A. King, W. Schaffer, C. Gordon, J. Treat, M. Kot] 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. Society for Mathematical Biology, 1996 King A. Program in Applied Mathematics, The University of Arizona, 85721, Tucson, AZ, U.S.A. aut Schaffer W. Program in Applied Mathematics, The University of Arizona, 85721, Tucson, AZ, U.S.A. aut Gordon C. Department of Ecology and Evolutionary Biology, The University of Arizona, 85721, Tucson, AZ, U.S.A. aut Treat J. Department of Ecology and Evolutionary Biology, The University of Arizona, 85721, Tucson, AZ, U.S.A. aut Kot M. Department of Mathematics, The University of Tennessee, 3796, Knoxville, TN, U.S.A. aut Bulletin of Mathematical Biology Kluwer Academic Publishers 58/5(1996-09-01), 835-859 0092-8240 58:5<835 1996 58 11538 https://doi.org/10.1007/BF02459486 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02459486 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- King A. Program in Applied Mathematics, The University of Arizona, 85721, Tucson, AZ, U.S.A aut NATIONALLICENCE 700 1- Schaffer W. Program in Applied Mathematics, The University of Arizona, 85721, Tucson, AZ, U.S.A aut NATIONALLICENCE 700 1- Gordon C. Department of Ecology and Evolutionary Biology, The University of Arizona, 85721, Tucson, AZ, U.S.A aut NATIONALLICENCE 700 1- Treat J. Department of Ecology and Evolutionary Biology, The University of Arizona, 85721, Tucson, AZ, U.S.A aut NATIONALLICENCE 700 1- Kot M. Department of Mathematics, The University of Tennessee, 3796, Knoxville, TN, U.S.A aut NATIONALLICENCE 773 0- Bulletin of Mathematical Biology Kluwer Academic Publishers 58/5(1996-09-01), 835-859 0092-8240 58:5<835 1996 58 11538 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer