Existence and globally asymptotical stability of periodic solutions for two-species non-autonomous diffusion competition n-patch system with time delay and impulses

Abstract

By using Mawhin continuation theorem and constructing suitable Lyapunov functional, a set of easily verifiable sufficient conditions ensuring the existence and global asymptotical stability of positive periodic solutions for two-species non-autonomous diffusion competition n-patch system with time delay and impulses are established. Finally, applications and an illustrative example are given. The main results generalize and improve the previously known results in Zhang and Wang (J. Math. Anal. Appl. 265:38–48, 2002), Dong et al. (Chaos Solitons Fractals 32:1916–1926, 2007).