一类稀疏效应下食饵-捕食系统极限环的存在唯一性

Existence and Uniqueness of Limit Cycle about Prey-Predator System with Sparssing Effect

本文研究如下一类具有稀疏效应的食饵－捕食模型ｄｘ／ｄｔ＝ｂｘ２（ｋ－ｘ）－ｂｘｙ，ｄｙ／ｄｔ＝－ｃｙ＋（βｘ－γｙ）ｙ。应用常微分方程定性理论，对该系统的平衡点进行分析，得到了该系统极限环存在唯一的充分条件，并给出了生态解释．

This paper is devoted to study the following prey-predator system model with sparssing effect dx/dt = bx2(k - x) - bxy, dy/dt = -cy + (βx - γy)y. by using qualitative theory of ordinary differential equations, we have analyzed the equilibrium points, obtained the sufficient conditions for the existence and uniqueness of limit cycle, and given some biological illustrations.