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本文通过生物控制和化学控制提出了具有周期脉冲效应与害虫控制的捕食系统. 系统保护天敌避免灭绝,在一些条件下可以使害虫灭绝.就是说当脉冲周期小于某一临界值时,存在全局稳定害虫灭绝周期解.脉冲周期增大大于临界值时,平凡害虫灭绝周期解失去稳定性并产生正周期解,利用分支理论来研究正周期解的存在性.进而,利用李雅普诺夫函数和比较定理确定了持续生存的条件.
In this paper, we propose a predator system with periodic pulse effect and pest control through biological control and chemical control, which protects the natural enemies from extinction and exterminates pests in some conditions, that is, when the pulse period is less than a certain critical value, there exists global stability Pest extinction periodic solution.When the pulse cycle increases larger than the critical value, the extinction of the ordinary pests loses its stability and leads to the positive periodic solution.The branch theory is used to study the existence of positive periodic solutions.Furthermore, by using the Lyapunov function and the comparison theorem Determine the conditions for sustained survival.