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首页> 外文期刊>Journal of Applied Mathematics and Computing >Dynamical analysis of a fuzzy phytoplankton-zooplankton model with refuge, fishery protection and harvesting
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Dynamical analysis of a fuzzy phytoplankton-zooplankton model with refuge, fishery protection and harvesting

机译：避难，渔业保护与收获的模糊浮游植物 - 浮游车模型的动态分析

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摘要

In this paper, a singular phytoplankton-zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy number. By using the utility function method, the transformed differential equation is reduced to a differential equation. In absence of economic profit, the existence of positive equilibria, local stability and global stability for the interior equilibrium of the present differential system are discussed, the conditions of Hopf bifurcation occurring at the positive equilibrium are given, and the corresponding nonlinear feedback controller is designed to eliminate Hopf bifurcation. In presence of economic profit, the corresponding differential algebraic model is proposed and some conditions of the existence of the interior equilibrium are derived. By regarding economic profit as bifurcation parameter, singular induced bifurcation occurring is investigated, and a linear controller is designed to remove such bifurcation. Furthermore, Pontryagin's maximum principle has been used to obtain optimal harvesting policy to maximize the benefit as well as conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical results after each part. Results show that imprecise parameters not only affect the interior equilibrium and the bionomic equilibrium of system, but also affect the critical value of bifurcation and branch range.
机译：在本文中，通过作为一种形式的三角模糊数来研究具有模糊参数，避难，渔业保护和收获的奇异浮游植物模型。通过使用本实用功能方法，将变换的微分方程减少到差分方程。在没有经济利润的情况下，讨论了存在正平平衡，局部稳定性和全局稳定性的本差分系统的内部平衡，给出了在正平平衡处发生的跳跃分叉的条件，设计了相应的非线性反馈控制器消除Hopf Burifation。在经济利润存在下，提出了相应的差分代数模型，衍生出内部平衡存在的一些条件。通过作为分叉参数的经济利润，研究了单数诱导的分叉发生，并且设计线性控制器以去除这种分叉。此外，Pontryagin的最大原则已被用来获得最佳的收获政策，以最大限度地提高益处和生态系统的保护。最后，给出了一些数值模拟，以证明在每个部分之后的理论结果。结果表明，不精确的参数不仅影响内部平衡和系统的直接性平衡，而且影响分支范围的临界值。

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