Dynamics of a new delayed stage-structured predator-prey model with impulsive diffusion and releasing. (English) Zbl 1418.92101
Summary: In this work, we propose a new delayed stage-structured predator-prey model with impulsive diffusion and releasing. By the stroboscopic map of the discrete dynamical system, we obtain a prey-extinction boundary periodic solution. Furthermore, we prove that the prey-extinction boundary periodic solution is globally attractive. We also prove that the investigated system is permanent by the theory on the delay and impulsive differential equations. Our results indicate that time delay, impulsive diffusion, and impulsive releasing have influence to the dynamical behaviors of the investigated system. The results of this paper also provide a tactical basis for pest management.
MSC:
| 92D25 | Population dynamics (general) |
| 34A37 | Ordinary differential equations with impulses |
| 37N25 | Dynamical systems in biology |
Keywords:
delayed stage structure; predator-prey model; impulsive diffusion; impulsive releasing; prey-extinctionReferences:
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