YUAN Hailong, LI Yanling*
(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
The existence and stability of positive solutions are investigated for a predator-prey model with Holling type Ⅲ functional response. By using the fixed point index in cones, one can reduce the sufficient conditions for any possible positive solutions. When m is suitably large,by the super-sub solution method for predator-prey systems, the positive solutions and the stability of the positive solutions are studied by using the linearized stability.It is shown that the models has coexistence solutions when a>λ1,c>λ1-dθ2a1+mθ2a and the coexistence solution is linear stability if c>λ1.
KeyWords:
predator-prey model; stability; fixed point index
