Permanence and global attractivity of an impulsive ratio-dependent predator–prey system in a patchy environment

This paper studies an impulsive nonautonomous two species predator–prey Lotka–Volterra type dispersal system in a patchy environment, in which the prey species can disperse among n different patches, but the predator species is confined to one patch and cannot disperse. On the basis of inequality estimation techniques and the comparison theory of impulsive differential equations, sufficient conditions of integrable form for the permanence and extinction are obtained. By constructing appropriate Lyapunov function, conditions for the global attractivity of the system are established.