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Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay
A nonautonomous diffusion model with Holling III
functional response and continuous time delay is considered in
this paper, where all parameters are time dependent and the prey
can diffuse between two patches of a heterogeneous environment
with barriers between patches, but for the predator the diffusion
does not involve a barrier between patches. It is shown that the
system is persistent under any diffusion rate effect. Moreover,
sufficient conditions that guarantee the existence of a positive
periodic solution which is globally asymptotic stable are
obtained.