Abstract
We investigate a predator‐prey model with impulsive diffusion on predator and stage structure on prey. The globally attractive condition of prey‐extinction periodic solution of the system is obtained by the stroboscopic map of the discrete dynamical system. The permanent condition of the system is also obtained by the theory of impulsive delay differential equation. The results indicate that the discrete time delay has influence on the dynamical behaviors of the system. Finally, some numerical simulations are carried out to support the analytic results.
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