Shaohong Cai

Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches

In this work, we propose a delayed predator-prey model with impulsively diffusive prey between two patches. Using the stroboscopic map of the discrete dynamical system, we obtain the globally attractive condition of predator-extinction periodic solution of the system. We also obtain the permanent condition of the system by the theory of impulsive delay differential equation. Our results indicate that the discrete time delay has influence to the dynamical behaviors of the system. Finally, the numerical analysis is inserted to illustrate the results.

DYNAMICAL ANALYSIS OF A THREE-DIMENSIONAL PREDATOR-PREY MODEL WITH IMPULSIVE HARVESTING AND DIFFUSION

In this work, we consider a three-dimensional predator-prey model with impulsive harvesting and diffusion at different fixed moments. We prove that all solutions of the investigated system are uniformly ultimately bounded. The conditions of the globally asymptotically stable prey-extinction boundary periodic solution of the investigated system are obtained, as well the permanence of the investigated system. Finally, numerical analysis is inserted to illustrate the results which provide reliable tactic basis for the practical biological resource management.

An SEIRS epidemic model with two delays and pulse vaccination

Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if RΔ < 1, and the infectious population is uniformly persistent if RΔ > 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.

Impulsive vaccination and dispersal on dynamics of an SIR epidemic model with restricting infected individuals boarding transports

Abstract To understand the effect of impulsive vaccination and restricting infected individuals boarding transports on disease spread, we establish an SIR model with impulsive vaccination, impulsive dispersal and restricting infected individuals boarding transports. This SIR epidemic model for two regions, which are connected by transportation of non-infected individuals, portrays the evolvement of diseases. We prove that all solutions of the investigated system are uniformly ultimately bounded. We also prove that there exists globally asymptotically stable infection-free boundary periodic solution. The condition for permanence is discussed. It is concluded that the approach of impulsive vaccination and restricting infected individuals boarding transports provides reliable tactic basis for preventing disease spread.

Dynamics of a periodic switched predator–prey system with impulsive harvesting and hibernation of prey population ☆

Abstract Winter hibernation constitutes an effective strategy of animals in order to correspond survive cold environments and limited availability of food, it plays an important role in biological evolution. In this work, we firstly introduce hibernation behaviors of prey population into predator–prey systems with impulsive effect, then construct a periodic switched predator–prey system with winter hibernation in prey population and impulsive effect. We prove that the solutions of system (2.1) are uniformly ultimately bounded. We obtain the conditions of the globally asymptotically stable predator-extinction boundary periodic solution of system (2.1) , and also obtain the permanent conditions of system (2.1) . Finally, numerical analysis is employed to illustrate the results. Our results provide reliable tactic for the biological economics management and the protection of biodiversity.

Dynamical analysis of a biological resource management model with impulsive releasing and harvesting

In this study, we consider a biological resource management predator-prey model with impulsive releasing and harvesting at different moments. First, we prove that all solutions of the investigated system are uniformly ultimately bounded. Second, the conditions of the globally asymptotic stability predator-extinction boundary periodic solution are obtained. Third, the permanence condition of the investigated system is also obtained. Finally, the numerical simulation verifies our results. These results provide reliable tactic basis for the biological resource management in practice.

Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment

In this work, we construct a stage-structured single population system with winter hibernation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population-extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.

Dynamical analysis on a single population model with state-dependent impulsively unilateral diffusion between two patches

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.