Analysis on stability of a ratio-dependent Holling-Leslie type predator-prey model
YANG Wenbin1*, WANG Yan′e2, LI Yanling3
(1 School of Science, Xi′an University of Posts and Telecommunications, Xi′an 710121, Shaanxi, China; 2 School of Computer Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China;3 School of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China)
Abstract:
A class of ratio-dependent Holling-Leslie type predator-prey model was studied in the paper.The stability of positive equilibrium for the local system is discussed by the method of spectral analysis. Meanwhile, the existence of periodic orbits is shown. Secondly, the Turing instability of the positive equilibrium for the reaction-diffusion system is also discussed by the same way, and then by the upper and lower solution method, the global stability is obtained.
KeyWords:
Holling-Leslie predator-prey model; reaction-diffusion system; stability
