在确定性和随机环境中,捕食者的捕获如何影响捕食者-猎物动力学?

IF 3.5 2区 数学 Q1 MATHEMATICS, APPLIED
Bapin Mondal , Sayan Mandal , Pankaj Kumar Tiwari , Ranjit Kumar Upadhyay
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引用次数: 0

摘要

本研究探讨了确定性和随机环境下捕食者-猎物相互作用的动力学,重点研究了捕食者捕获的生态影响。理论和数值分析探讨了局部稳定性,分岔和生物平衡,以确定可持续的收获策略。我们的研究结果表明,增加捕食者的捕获率可以通过鞍节点分叉诱导多达四个内部平衡点,包括破坏系统稳定的灾难性转变。在高收获率下,无捕食者平衡变得全局稳定,而低和中等收获率导致双稳定或三稳定,允许猎物和捕食者种群共存。对于随机模型,我们推导了物种持续和灭绝的条件,使用置信椭圆方法量化触发稳定状态之间临界转换的阈值噪声强度。在低噪音水平下,捕食者和猎物的数量会在稳定的平衡状态下波动,但较高的噪音强度会导致交替状态或捕食者灭绝。影响系统动力学的关键因素包括捕食者的内在生长率、替代食物来源和收获强度。我们的分析强调了生态系统对随机干扰的脆弱性,并强调了精心管理采伐实践的重要性。这些发现有助于制定平衡生态稳定与经济目标的策略,确保捕食者-猎物种群的长期可持续性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
How predator harvesting affects prey-predator dynamics in deterministic and stochastic environments?
This study investigates the dynamics of predator-prey interactions in both deterministic and stochastic environments, with a focus on the ecological implications of predator harvesting. Theoretical and numerical analyses explore local stability, bifurcations, and bionomic equilibria to identify sustainable harvesting strategies. Our findings reveal that increasing predator harvesting rates can induce up to four interior equilibrium points via saddle-node bifurcations, including catastrophic transitions that destabilize the system. At high harvesting rates, the predator-free equilibrium becomes globally stable, while low and intermediate rates result in bistability or tristability, allowing coexistence of prey and predator populations. For the stochastic model, we derive conditions for species persistence and extinction, using the confidence ellipse method to quantify threshold noise intensities that trigger critical transitions between stable states. At low noise levels, predator and prey populations fluctuate around stable equilibria, but higher noise intensities can drive shifts to alternate states or predator extinction. The key factors influencing system dynamics include the predator's intrinsic growth rate, alternative food sources, and harvesting intensity. Our analysis underscores the vulnerability of ecological systems to stochastic disturbances and emphasizes the importance of carefully managed harvesting practices. These findings contribute to the development of strategies that balance ecological stability with economic objectives, ensuring the long-term sustainability of predator-prey populations.
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来源期刊
CiteScore
7.90
自引率
10.00%
发文量
755
审稿时长
36 days
期刊介绍: Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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