Uniqueness of limit cycles in Gause-type models of predator-prey systems

Mathematical Biosciences - Tập 88 Số 1 - Trang 67-84 - 1988
Yang Kuang1, H. I. Freedman1
1Department of Mathematics University of Alberta Edmonton, Canada T6G 2G1#TAB#

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Tài liệu tham khảo

Albrecht, 1973, Stable limit cycles in prey-predator populations, Science, 181, 1073, 10.1126/science.181.4104.1073

Armstrong, 1976, The effects of predator functional response and prey productivity on predator-prey stability: A graphical approach, Ecology, 57, 609, 10.2307/1936446

Armstrong, 1976, Fugitive species: Experiments with fungi and some theoretical considerations, Ecology, 57, 953, 10.2307/1941060

Armstrong, 1979, Prey species replacement along a gradient of nutrient enrichment: A graphical approach, Ecology, 60, 76, 10.2307/1936470

Cheng, 1981, Uniqueness of a limit cycle for a predator-prey system, SIAM J. Math. Anal., 12, 541, 10.1137/0512047

Cheng, 1981, Some results on global stability of a predator-prey system, J. Math. Biol., 12, 115, 10.1007/BF00275207

Cherkas, 1970, Some tests for the absence or uniqueness of limit cycles, Differential Equations, 6, 891

Freedman, 1980

Freedman, 1985, Global stability and persistence of simple food chains, Math. Biosci., 76, 69, 10.1016/0025-5564(85)90047-1

Freedman, 1975, Perturbation of two dimensional predator-prey equations, SIAM J. Appl. Math., 28, 1, 10.1137/0128001

Freedman, 1975, Perturbation of two dimensional predator-prey equations with an unperturbed critical point, SIAM J. Appl. Math., 29, 719, 10.1137/0129060

Gause, 1936, Further studies of interaction between predator and prey, J. Animal Ecol., 5, 1, 10.2307/1087

Goh, 1978, Global stability in a class of predator-prey models, Bull. Math. Biol., 40, 525, 10.1007/BF02460776

Hartman, 1964

Hassell, 1978

Hassell, 1973, Stability in insect host-parasite models, J. Animal Ecol., 42, 693, 10.2307/3133

Hsu, 1978, On the global stability of a predator-prey system, Math. Biosci., 39, 1, 10.1016/0025-5564(78)90025-1

L.-P. Liou and K.-S. Cheng, On the uniqueness of a limit cycle for a predator-prey system, to appear.

May, 1972, Limit cycles in predator-prey communities, Science, 177, 900, 10.1126/science.177.4052.900

Rosenzweig, 1969, Why the prey curve has a bump, Amer. Nat., 103, 81, 10.1086/282584

Rosenzweig, 1971, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science, 171, 385, 10.1126/science.171.3969.385

Rosenzweig, 1973, Evolution of the predator isocline, Evolution, 27, 84, 10.2307/2407121

Waltman, 1983

Ye, 1986

Zhang, 1986, Proof of the uniqueness theorem of limit cycles of generalized Lienard equations, Appl. Anal., 23, 63, 10.1080/00036818608839631