An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

最佳综合虫害管理的期望是释放天敌的瞬时数量应取决于田间虫害和天敌的密度。为此，提出了具有非线性脉冲控制策略的广义捕食者—食饵模型，并对其动力学进行了研究。基于Floquet定理和解析方法，获得了无虫周期溶液全局稳定性的阈值条件。另外，给出了永久性的充分条件。此外，通过显示模型的频闪图的非平凡固定点是否存在，该时间点由等于普通脉冲周期的时间快照确定，从而确定了找到非平凡周期性解的问题。为了解决非线性脉冲控制对害虫动力学和成功害虫控制的影响，以捕食者-猎物模型为例，该模型以Holling II型功能响应函数为例进行了研究。最后，数值模拟表明，所提出的模型具有非常复杂的动力学行为，包括周期倍增分叉，混沌解，混沌危机，周期减半分叉和周期窗口。此外，存在一个有趣的现象，当采用非线性脉冲控制时，周期加倍分支和周期减半分支总是共存，这使得模型的动力学行为更加复杂，从而在设计成功的害虫控制策略时造成了困难。以Holling II型功能响应函数为例，研究了捕食者与被捕食者的模型。最后，数值模拟表明，所提出的模型具有非常复杂的动力学行为，包括周期倍增分叉，混沌解，混沌危机，周期减半分叉和周期窗口。此外，存在一个有趣的现象，当采用非线性脉冲控制时，周期加倍分支和周期减半分支总是共存，这使得模型的动力学行为更加复杂，从而在设计成功的害虫控制策略时造成了困难。以结合Holling II型功能响应函数的捕食者-被捕食者模型为例进行了研究。最后，数值模拟表明，该模型具有非常复杂的动力学行为，包括周期倍增分叉，混沌解，混沌危机，周期减半分叉和周期窗。此外，存在一个有趣的现象，当采用非线性脉冲控制时，周期加倍分支和周期减半分支总是共存，这使得模型的动力学行为更加复杂，从而在设计成功的害虫控制策略时造成了困难。周期减半分叉和周期性窗口。此外，存在一个有趣的现象，当采用非线性脉冲控制时，周期加倍分支和周期减半分支总是共存，这使得模型的动力学行为更加复杂，从而在设计成功的害虫控制策略时造成了困难。周期减半分叉和周期性窗口。此外，存在一个有趣的现象，当采用非线性脉冲控制时，周期加倍分支和周期减半分支总是共存，这使得模型的动力学行为更加复杂，从而在设计成功的害虫控制策略时造成了困难。