The dynamic behaviors of one-predator two-prey system with mutual interference and impulsive control. (English) Zbl 1540.34048
Summary: Taking into account chemical control, biological control for pest management at different fixed moments, and mutual interference of the predator. A one-predator two-prey system with impulsive effects and mutual interference is established in this paper. By using techniques of impulsive perturbations, Floquet theory and comparison theorem, we investigate the existence and globally asymptotic stability of prey-eradication periodic solution. We also derive some sufficient conditions for the permanence of the system by using comparison methods involving multiple Lyapunov functions. Our results improve some obtained results. Then numerical simulations are given to show the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies.
MSC:
| 34A37 | Ordinary differential equations with impulses |
| 92D25 | Population dynamics (general) |
| 34H05 | Control problems involving ordinary differential equations |
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