一类捕食者-食饵系统的全局结构
Global Structure of a Kind of Predator-Prey System
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摘要: 本文中我们证明了关于一般捕食者-食饵系统不存在闭轨线的定理,即文中定理2.应用这一定理和关于捕食者-食饵系统极限环的存在唯一性定理[1],我们完成了在各种参数条件对一个具体的捕食者-食饵系统模型[2]的研究.Abstract: In this paper we prove a theorem, theorem 2, on nonexistence of closed trajectory for a general predator-prey system.Then, using this theorem and another theorem on existence and uniqueness of limit cycle for predator-prey system[1], we complete the investigation of a concrete model of predator-prey system[2] under the conditions of all kinds of parameters.
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[1] 丁孙荭,捕食者-食饵(predator-prey)系统极限环的唯一性,科学通报,13 (1985),785-788. [2] Hsu, S.B., S.P. Hubbell and P. Waltman, Competing predator, SIAM, J. Appl. Math., 85(1978), 617-625. [3] Hastings, Alan, Global stability of two species systems, J. Math. Biology, 5(1978), 399-403. [4] Cheng Kuo-sheng, Uniqueness of limit cycle for a predator-prey system, SIAM, J. Math. Anal, 12, 4(1981), 541-548. -
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