研究生态动态系统中的全局稳定性和分岔问题

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-06-05 DOI:10.1155/2024/4970657
Muhammad Salman Khan, Rizwan Niaz, Mohammed Ahmed Alomair, Mohamed Hussien
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引用次数: 0

摘要

我们考虑了一个连续时间模型,该模型使用霍林 II 型响应来描述浮游植物和浮游动物之间的相互作用。然后,我们使用分数阶离散化方法将该连续时间模型转化为离散时间模型。本文探讨了所获系统关于所有平衡点的局部稳定性,并确定了其正定点的全局渐近稳定性。研究还证明,在特定的数学条件下,该系统会在其正平衡点附近发生 Neimark-Sacker 分岔。为了有效控制这种分岔,本文引入了两种改进的混合控制技术。论文最后通过举例说明,验证了理论结论,并评估了新提出的控制策略的有效性和可行性。此外,还对改进的混合技术和现有的混合方法进行了对比分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Investigating Global Stability and Bifurcation in an Ecological Dynamical System

Investigating Global Stability and Bifurcation in an Ecological Dynamical System

We consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability of this obtained system concerning all equilibrium points and establishes the global asymptotic stability of its positive fixed point. The study also demonstrates that, under specific mathematical conditions, the system undergoes a Neimark–Sacker bifurcation around its positive equilibrium point. To effectively manage this bifurcation, two modified hybrid control techniques are introduced. The paper concludes by presenting illustrative numerical examples that validate the theoretical findings and assess the effectiveness and feasibility of the newly proposed control strategies. In addition, a comparative analysis is conducted between the modified hybrid techniques and an existing hybrid approach.

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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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