一类具功能反应的食饵-捕食系统的定性分析

Qualitative Analysis for a Kind of Predator- prey Systems with Functional Response

研究一类具功能反应的食饵-捕食系统:x=xg(x)-yφ(x),y=y(-d+eφ(x))在g(x)=a-bxα2-cxα,φ(x)=kxα及23≤α<1情形下,分析了该系统的平衡点性态,运用Dulac判别法和Poincare-Bendixson环域定理得出系统极限环不存在性及存在性的条件。

A kind of predator- prey systems with functional response is investigated in the paper： x = xg（x） - yφ（ x ） , y = y（ - d ＋ eφ（ x ） ） in condition of g（x） = a - bx - cx φ（ x ） = kx and 2/3≤a 〈 1 , the quality of the equilibrium point is discussed. Besides, the conditions for nonexistence and existence of the limit cycle are obtained by the method of Dulac function and Poincare - Bendixson theory.