Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava
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We observe that the model system undergoes a sequence of codimension one and codimension two bifurcations. Our results show that in the absence of predator harvesting, increasing levels of fear destabilize the predator–prey system, and controlled harvesting is beneficial for the coexistence of both populations. Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost‐functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. It is observed that implementing optimal harvesting not only contributes to the ecological benefits by maintaining a sustainable balance of predator–prey evolution but also plays a significant role in maximizing the economic benefits.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear dynamics in a fear‐driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting\",\"authors\":\"Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava\",\"doi\":\"10.1002/mma.10431\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. 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Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost‐functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. 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引用次数: 0
摘要
捕食者驱动的恐惧对生态系统的影响是巨大的,既包括营养(直接)效应,也包括非营养(间接)效应。以往的研究表明,非营养性恐惧效应在捕食者-猎物动态中具有重要作用。本研究调查了通食性捕食者对猎物的非营养性恐惧效应,并探讨了最佳捕食方式。我们假设猎物的繁殖率会因恐惧效应而降低,且通性捕食者遵循霍林 II 型捕食策略进行捕食。此外,我们还假设捕食者具有商业价值,并根据其密度按比例捕获。我们证明了平衡点的存在、其局部和全局稳定性以及分岔分析。我们观察到,模型系统经历了一连串标度为一和标度为二的分岔。我们的研究结果表明,在没有捕食者捕杀的情况下,恐惧程度的增加会破坏捕食者-猎物系统的稳定性,而有控制的捕杀有利于两个种群的共存。此外,捕食者的捕杀可能会产生九头蛇效应和多重九头蛇效应。我们发现了不同类型的双稳态现象,强调了初始种群数量的重要性。此外,我们还通过提出一个最优控制问题(OCP)来探索最优捕获策略。收割成本函数的设计结合了仿生平衡状态。我们利用庞特里亚金最大原则,对 OCP 进行数值求解。结果表明,实施最优捕捞不仅能通过维持捕食者-猎物进化的可持续平衡来提高生态效益,而且还能在最大化经济效益方面发挥重要作用。
Nonlinear dynamics in a fear‐driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting
The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores optimal harvesting. We assume that the reproduction rate of prey is reduced due to the fear effect, and generalist predator follows Holling type II foraging strategy for predation. Additionally, we assume that predators are commercially valuable and harvested proportionately to their density. We demonstrate the existence of equilibrium points, their local and global stability, and bifurcation analysis. We observe that the model system undergoes a sequence of codimension one and codimension two bifurcations. Our results show that in the absence of predator harvesting, increasing levels of fear destabilize the predator–prey system, and controlled harvesting is beneficial for the coexistence of both populations. Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost‐functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. It is observed that implementing optimal harvesting not only contributes to the ecological benefits by maintaining a sustainable balance of predator–prey evolution but also plays a significant role in maximizing the economic benefits.