Existence and uniqueness of positive solution for a predator-prey model with C-M type functional response
LI Haixia1,2, LI Yanling1*
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China;2 Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013, Shaanxi, China)
Abstract:
Existence and uniqueness of positive solution for a one-prey and two-competing-predators system with C-M type functional response are considered.The existence of positive solution is discussed by means of the fixed point index theory and sufficient conditions:r>λ1,-m1>λ1e1-p11+b1,-m2>λ1e2-p21+b2 for the existence of coexistence states are determined. In addition, the stability and uniqueness of positive solution are investigated by using the stability theorem and degree theory.
KeyWords:
predator-prey model; fixed point index; stability; uniqueness
