Graph-theoretic method on the periodicity of multipatch dispersal predator-prey system with Holling type-II functional response

We study the periodicity of multipatch dispersal predator-prey system with Holling type-II functional response in this paper. By providing a new method, we overcome the difficulty to get the priori bounds estimation of unknown solutions of operator equation Lu=λNu. Graph theory with coincidence degree theory is used, and a sufficient criterion for the periodicity of the system is obtained. The criterion presented in this paper is closely related with topological structure of dispersal network and can be verified easily. Finally, a numerical example is also provided to verify the effectiveness of theoretical results.