Abstract
In this paper, infinite delays and prey dispersal on a network are considered in multi-patch periodic predator–prey systems. Novel graph-theoretic method is adopted to estimate the uniform upper bounds of unknown solutions to operator equation Lu=λNu. The existence criterion of positive periodic solutions to coupled predator–prey systems is obtained by using classic coincidence degree theory, which is closely related to prey dispersal network in a patch environment. Finally, two numerical examples are also shown to illustrate the effectiveness of theoretical results.
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