The characteristics study of a bounded fractional-order chaotic system: Complexity, and energy control

IF 6.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY alexandria engineering journal Pub Date : 2024-10-30 DOI:10.1016/j.aej.2024.10.038

Qingzhe Wu , Juling Zhang , Miao Li , Hassan Saberi-Nik , Jan Awrejcewicz

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Abstract

The dynamics of a four-dimensional fractional-order (FO) dynamical system from the viewpoint of spectral entropy (SE), C

_{0}

complexity, and algorithm 0–1 are presented in detail in this article. The efficiency of these algorithms in the existence of chaos for FO systems has been investigated as well as other methods such as Lyapunov exponents, Lyapunov dimension, and bifurcation diagrams. With Hamilton’s energy analysis for the 4D FO system, it is found that chaotic behavior is more dependent on energy consumption. Therefore, it is necessary to design a negative feedback control to reduce energy consumption and suppress chaotic behavior. Finally, we obtain the global Mittag-Leffler positive invariant sets (GMLPISs) and global Mittag-Leffler attractive sets (GMLASs) of the introduced system. Numerical results indicate the effectiveness of complexity and chaos detection methods as well as bound calculation.

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有界分数阶混沌系统的特性研究：复杂性与能量控制

本文从谱熵 (SE)、C0 复杂性和算法 0-1 的角度详细介绍了四维分数阶（FO）动力系统的动力学。研究了这些算法在 FO 系统存在混沌时的效率，以及其他方法，如 Lyapunov 指数、Lyapunov 维度和分岔图。通过对 4D FO 系统进行汉密尔顿能量分析，发现混沌行为更依赖于能量消耗。因此，有必要设计一种负反馈控制来减少能量消耗并抑制混沌行为。最后，我们得到了引入系统的全局 Mittag-Leffler 正不变集（GMLPISs）和全局 Mittag-Leffler 吸引集（GMLASs）。数值结果表明了复杂性和混沌检测方法以及约束计算的有效性。

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来源期刊

alexandria engineering journal Engineering-General Engineering

CiteScore

11.20

自引率

4.40%

发文量

1015

审稿时长

43 days

期刊介绍： Alexandria Engineering Journal is an international journal devoted to publishing high quality papers in the field of engineering and applied science. Alexandria Engineering Journal is cited in the Engineering Information Services (EIS) and the Chemical Abstracts (CA). The papers published in Alexandria Engineering Journal are grouped into five sections, according to the following classification: • Mechanical, Production, Marine and Textile Engineering • Electrical Engineering, Computer Science and Nuclear Engineering • Civil and Architecture Engineering • Chemical Engineering and Applied Sciences • Environmental Engineering