Analysis and Synchronization of the Chen System with Fractional Derivative

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2024-05-23 DOI:10.1142/s0218127424500883

Chuntao Yin, Yufei Zhao, Xianghong Li, Yongjun Shen

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Abstract

In this paper, we study the dynamic behaviors and chaos synchronization of the Chen system described by Caputo–Hadamard fractional derivative. First, the existence and uniqueness of a solution to the Chen system with Caputo–Hadamard derivative are proved by qualitative analysis. Further, the stability of equilibria of the considered system is analyzed with the aid of Routh–Hurwitz criteria. Meanwhile, the bifurcation condition of the Caputo–Hadamard Chen system is compared with the integer-order Chen system, where the differences between the two systems are demonstrated numerically. In the study of chaos synchronization of the drive–response Chen systems with Caputo–Hadamard derivative, two control schemes are developed: three nonlinear controllers and single linear controller. The feasibility of two control schemes is verified, and the synchronization performances of these two schemes are compared by numerical simulations. Based on this, the influence of the fractional-order on chaos synchronization performance is illustrated as well.

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带分数微分的陈氏系统的分析和同步化

本文研究了用 Caputo-Hadamard 分数导数描述的 Chen 系统的动态行为和混沌同步。首先，通过定性分析证明了具有 Caputo-Hadamard 导数的 Chen 系统解的存在性和唯一性。此外，还借助 Routh-Hurwitz 准则分析了所考虑系统平衡点的稳定性。同时，将 Caputo-Hadamard Chen 系统的分岔条件与整数阶 Chen 系统进行了比较，并用数值证明了两个系统之间的差异。在研究具有 Caputo-Hadamard 导数的驱动响应 Chen 系统的混沌同步时，提出了两种控制方案：三个非线性控制器和一个线性控制器。验证了两种控制方案的可行性，并通过数值模拟比较了这两种方案的同步性能。在此基础上，还说明了分数阶对混沌同步性能的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.