A multi-state dependent model is proposed for integrated pest management, which adopts different control methods at different thresholds. The sufficient conditions for the existence of order one periodic solution to t...A multi-state dependent model is proposed for integrated pest management, which adopts different control methods at different thresholds. The sufficient conditions for the existence of order one periodic solution to the system are obtained by using differential equation geometry theory and successor function. Furthermore, we have discussed the existence of order-k (k ≥ 2) periodic solution by using series convergence. Besides we have proved the order one periodic solution is orbitally asymptotically stable under certain conditions with analogue of the Poincare criterion. Finally, numerical simulations are given to show the feasibility of our main results. Especially, the proved process of the existence of order one periodic solution shows that our method used in this paper is easier than the existing methods.展开更多
文摘A multi-state dependent model is proposed for integrated pest management, which adopts different control methods at different thresholds. The sufficient conditions for the existence of order one periodic solution to the system are obtained by using differential equation geometry theory and successor function. Furthermore, we have discussed the existence of order-k (k ≥ 2) periodic solution by using series convergence. Besides we have proved the order one periodic solution is orbitally asymptotically stable under certain conditions with analogue of the Poincare criterion. Finally, numerical simulations are given to show the feasibility of our main results. Especially, the proved process of the existence of order one periodic solution shows that our method used in this paper is easier than the existing methods.
