一类具有Allee效应的害虫综合治理捕食-食饵模型的动力学分析

Dynamical Analyses of an Integrated Pest Management Predator-prey Model with Allee Effect

  • 摘要: 考虑了一类具有状态反馈脉冲控制和Allee效应的捕食-食饵模型,其中天敌的投放量及杀虫剂的使用强度均线性依赖于害虫的控制水平.首先,分析了无控制系统解的正性及有界性,并给出了正平衡态全局渐近稳定的充分条件.其次,借助于后继函数方法讨论了控制系统阶1周期解的存在性,并给出了阶1周期解稳定的条件.为了确定最佳的天敌投放量和杀虫剂强度,以投入成本最小化为目标进行了优化模型构建与分析.结果表明,基于本文所提出的控制策略,害虫数量可控制在经济损害水平之下并呈周期性变化.

     

    Abstract: A class of predator-prey model with impulsive state feedback control and Allee effect on predator is considered, where the quantity of natural enemies released and the intensity of pesticide sprayed linearly depend on the pest control level. Firstly, the positivity and boundedness on the solutions of uncontrollable system were analyzed, and the sufficient conditions for global asymptotic stability of the positive equilibrium were given. Secondly, the existence of the order-1 periodic solution of the control system was discussed by means of the success function method, and the condition for the stability of the order-1 periodic solution was given. In order to determine the optimal quantity of natural enemies released and the intensity of pesticide sprayed, the optimization model is constructed and analyzed with the aim of minimizing input cost. The results showed that, based on the control strategy proposed, the number of pests can be limited to below an economic threshold and displays periodic variation.

     

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