A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic soluti...A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.展开更多
A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution...A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.展开更多
基金Supported by National Natural Science Foundation of China (No.10171106)
文摘A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.
基金This work is supported by National Natural Science Foundation of China (10171106)supported by ScienceResearch Project Foundation of Liaoning Province Education Department
文摘A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.
