一般脉冲生物控制模型的全局稳定性与优化
Global stability and optimisation of a general impulsive biological control model
摘要：
考虑一类脉冲增广生物控制模型，该模型由一般的连续捕食-食饵常微分方程模型和描述捕食者周期性引入的离散增广部分组成.证明了该系统存在一个与食饵根除相对应的不变周期解，并给出了保证其全局渐近稳定性的条件。然后考虑与抢先使用增强生物控制有关的优化问题。假设生物防治的单位时间预算（即释放的捕食者数量）是固定的，并在释放频率方面寻求该预算的最佳部署。要最小化的费用函数是将不可预见的猎物（害虫）入侵减少到某一无害水平所花费的时间。分析表明，优化问题承认一个可数无穷多个解决方案。考虑所需的鲁棒性的优化结果的论证，然后进行，它表明，最好的部署是使用尽可能频繁（因此尽可能小）的捕食者介绍。
英文摘要：
An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations augmented by a discrete part describing periodic introductions of predators is considered. It is shown that there exists an invariant periodic solution that corresponds to prey eradication and a condition ensuring its global asymptotic stability is given. An optimisation problem related to the preemptive use of augmentative biological control is then considered. It is assumed that the per time unit budget of biological control (i.e. the number of predators to be released) is fixed and the best deployment of this budget is sought after in terms of release frequency. The cost function to be minimised is the time taken to reduce an unforeseen prey (pest) invasion under some harmless level. The analysis shows that the optimisation problem admits a countable infinite number of solutions. An argumentation considering the required robustness of the optimisation result is then conducted and it is shown that the best deployment is to use as frequent (and thus as small) as possible predator introductions.
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