具非单调增长率和功能反应的食饵-捕食者模型的定性分析  

QUALITATIVE ANALYSIS OF A KIND OF PREDATOR-PREY SYSTEM WITH NON-MONOTONY INCREASE RATE AND FUNCTIONAL RESPONSE

作　　者：彭卫丽[1] 卢琨[1] 王莉[1] 

机构地区：[1]陕西科技大学理学院,陕西西安710021

出　　处：《陕西科技大学学报（自然科学版）》2008年第5期134-138,共5页Journal of Shaanxi University of Science & Technology

摘　　要：研究了一类具非单调增长率和功能反应的食饵-捕食者系统,.=x[a-bx-h(x)]-kyx^(1/2),=y[-d+kex],先用微分方程稳定性和定性理论讨论了该系统存在正平衡点的条件,再构造Dulac函数给出了该系统极限环不存在的相关条件,最后用Poincare-Bendixson环域定理和张芷芬惟一性定理,证明了该系统在不稳定的正平衡点周围存在唯一的极限环,最后用Matlab数值模拟对结果进行了验证,推广了已有的一些结论.Considering a kind of prey-predator system which the prey have non-monotony increase rate and the predator have a functional response.,x^＊=x[a-bx-h（x）]-ky√x,y^＊=y[-d＋ke√x],The quality of the equilibrium in this system is expounded by using the stability and qualitative theory of the ordinary difference equation, then the conditions for nonexistence, existence, uniqueness and the global stability of the limit cycle are proved, and validates the conclusions by plotting with Matlab. Thus some former conclusions are extended.

关 键 词：平衡点 DULAC函数 全局稳定 极限环 

分 类 号：O175.12[理学—数学]