标题： 关于基因型结构捕食者-猎物系统最优控制的生态救援和振荡恢复 显示英文标题

标题： On Optimal Control of a Genotype-Structured Prey-Predator System for Ecological Rescue and Oscillation Restoration

摘要： 进化改变影响种群间的相互作用，并可能通过导致灭绝或破坏种群振荡来扰乱生态系统，对生物多样性保护构成重大挑战。 本研究利用最优控制方法探讨了被突变猎物种群威胁的捕食者种群的生态救援问题。 为了研究这一问题，我们提出了一种模型，该模型包含了基因型结构化的猎物种群，包括野生型、杂合子和突变型猎物类型以及捕食者种群。 我们证明了该模型具有局部和全局解的存在性和唯一性，确保了模型的鲁棒性。 随后，我们应用最优控制方法结合庞特里亚金最大原理，在模型中引入控制输入以最小化突变种群数量并最终稳定生态系统。 数值结果清楚地表明，可以通过控制模型中的不利动态来实现突变种群的抑制，拯救捕食者，并恢复系统的振荡动态。 这些发现展示了控制策略的有效性，并为管理此类生态扰动提供了数学框架。 显示英文摘要

摘要： Evolutionary changes impacts interactions among populations and can disrupt ecosystems by driving extinctions or by collapsing population oscillations, posing significant challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using optimal control method. To study this, we proposed a model which incorporates genotypically structured prey comprising of wild-type, heterozygous and mutant prey types and predator population. We proved that this model has both local and global existence and uniqueness of solutions ensuring the model robustness. Then, we applied optimal control method along with Pontryagin Maximum Principle by incorporating a control input in the model to minimize the mutant population and subsequently to stabilize the ecosystem. The numerical results clearly reveal that the undesired dynamics of the model can be controlled showing the suppression of the mutant, rescues the predator, and restores the oscillatory dynamics of the system. These findings demonstrate the efficacy of the control strategy and provide a mathematical framework for managing such ecological disruptions