The dynamics of an epidemic model for pest control with impulsive effect |
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Authors: | Limin Wang Lansun Chen Juan J Nieto |
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Institution: | 1. Department of Mathematics and Physics, Dalian Jiaotong University, 116028 Dalian Liaoning, PR China;2. Department of Applied Mathematics, Dalian University of Technology, 116024 Dalian Liaoning, PR China;3. Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de, Santiago de Compostela, 15782 Santiago de Compostela, Spain |
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Abstract: | In pest control, there are only a few papers on mathematical models of the dynamics of microbial diseases. In this paper a model concerning biologically-based impulsive control strategy for pest control is formulated and analyzed. The paper shows that there exists a globally stable susceptible pest eradication periodic solution when the impulsive period is less than some critical value. Further, the conditions for the permanence of the system are given. In addition, there exists a unique positive periodic solution via bifurcation theory, which implies both the susceptible pest and the infective pest populations oscillate with a positive amplitude. In this case, the susceptible pest population is infected to the maximum extent while the infective pest population has little effect on the crops. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamic, which implies that this model has more complex dynamics, including period-doubling bifurcation, chaos and strange attractors. |
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