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Global stability and bifurcation analysis of a delay induced prey-predator system with stage structure

机译：一类具有阶段结构的时滞捕食系统的全局稳定性与分岔分析。

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This paper describes a delay induced prey-predator system with stage structure for prey. The dynamical characteristics of the system are rigorously studied using mathematical tools. The coexistence equilibria of the system is determined and the dynamic behavior of the system is investigated around coexistence equilibria. Sufficient conditions are derived for the global stability of the system. The optimal harvesting problem is formulated and solved in order to achieve the sustainability of the system, keeping the ecological balance, and maximize the monetary social benefit. Maturation time delay of prey is incorporated and the existence of Hopf bifurcation phenomenon is examined at the coexistence equilibria. It is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Moreover, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations.
机译：本文描述了具有阶段性结构的被捕食者的时滞诱导捕食系统。使用数学工具严格研究了系统的动态特性。确定系统的共存平衡，并围绕共存平衡研究系统的动态行为。得出了系统整体稳定性的充分条件。为了实现系统的可持续性，保持生态平衡并最大化货币社会效益，制定并解决了最佳收获问题。引入了捕食者的成熟时间延迟，并在共存平衡下研究了Hopf分叉现象的存在。结果表明，时间延迟会导致稳定的平衡变得不稳定，甚至导致稳定性的切换。此外，我们使用范式和中心流形定理来检验Hopf分支的性质。最后，给出了一些数值模拟以验证分析结果，并通过图形化图示对系统进行了分析。

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