Title :
Global stability analysis for a two species predator-prey model with dispersal for predators among patches and holling type II functional response
Author_Institution :
Dept. of Math., Daqing Normal Univ., Daqing, China
Abstract :
In this paper, we investigate a two species predator-prey model with dispersal and Holling type II functional response for predators among n patches. Our main purpose is to extend the global stability criteria by Li and Shuai(2010) on a predator-prey model with dispersal for preys among n patches. Firstly, by using the basic reproduction number and uniform persistence theory, we obtain the threshold dynamics of the system, that is, the system is uniformly persistent and there exists at least one coexistence equilibrium if the basic reproduction number is larger than one unit. Secondly, by using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, we derive sufficient conditions that the positive coexistence equilibrium of the coupling model is unique and global asymptotically stable.
Keywords :
Lyapunov methods; asymptotic stability; graph theory; predator-prey systems; Lyapunov functions; basic reproduction number; coexistence equilibrium; dispersal functional response; global asymptotic stability; global stability analysis; global stability criteria; graph-theoretical approach; holling type II functional response; predator-prey model; sufficient conditions; threshold dynamics; uniform persistence theory; Asymptotic stability; Biological system modeling; Couplings; Lyapunov methods; Predator prey systems; Stability criteria; Functional response; Global stability; Holling type II; Patchy dispersal; Predator-prey model; Uniform persistence;
Conference_Titel :
Control and Decision Conference (CCDC), 2015 27th Chinese
Conference_Location :
Qingdao
Print_ISBN :
978-1-4799-7016-2
DOI :
10.1109/CCDC.2015.7162748
