一类稀疏效应下食饵-捕食系统的极限环的存在唯一性

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

研究如下一类具稀疏效应的食饵-捕食模型dxdt=x2(e-bx)-dxy,dydt=-cy+(βx2-ry)y.应用常微分方程定性理论,对该系统的平衡点进行分析,得到了极限环存在唯一性及不存在的参数范围.

This paper is devoted to study the following prey-predator system model with sparssing efffect. dx/dt=x^2（e-bx）-dxy,dy/dt=-cy＋（βx^2-ry）y. By using qualitative theory of ordinary differential equations, we have analyzed the equilibrium points, obtained the parameter region of the existence, uniqueness and nonexistence of limit cycle of the above system.