Abstract
Coupling with social progress, traffic development and so on, the natural environment is going into patches. There are differences between population in differential patches. The population living in a patchy environment is affected by the space structures. It is important to depict the dynamical behaviors of the population in the present world. In this work, a state-dependent impulsive differential model, which focuses on impulsively unilateral diffusion between two patches, aims for the simulation of the factual population dynamical behaviors. With the approaches of mathematical analysis, we obtain sufficient conditions of the existence and orbitally asymptotic stability of a periodic solution of the investigated system. Finally, the numerical simulations verify our results.
Highlights
1 Introduction The population diffusion affecting the dynamical behaviors of populations in differential patches are investigated by many researchers [ – ]
Jiao et al [ ] devoted their work to investigation of the dynamics of a stage-structured predator-prey model with prey impulsively diffusing between two patches, they did not propose a single population model with statedependent impulsively unilateral diffusion between two patches
In Section, we give the sufficient conditions of the existence and orbitally asymptotic stability of a periodic solution of the investigated system
Summary
1 Introduction The population diffusion affecting the dynamical behaviors of populations in differential patches are investigated by many researchers [ – ]. Jiao et al [ ] devoted their work to investigation of the dynamics of a stage-structured predator-prey model with prey impulsively diffusing between two patches, they did not propose a single population model with statedependent impulsively unilateral diffusion between two patches. Motivated by these biological facts and the previous studies, we propose and investigate a state-dependent impulsive differential model, which focuses on impulsively unilateral diffusion between two patches. In Section , we give the sufficient conditions of the existence and orbitally asymptotic stability of a periodic solution of the investigated system.
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