Simulation of fractional order chaotic oscillators applying the Grünwald–Letnikov definition and the Adams–Bashforth–Moulton method

IF 2.2 3区工程技术 Q3 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Integration-The Vlsi Journal Pub Date : 2025-01-27 DOI:10.1016/j.vlsi.2025.102366

Alejandro Silva-Juarez , Sergio A. Rosales-Nunez , Luis C. Alvarez-Simon , Gregorio Zamora-Mejia , Victor H. Carbajal-Gomez , Alejandro I. Bautista-Castillo , Jose M. Rocha-Perez

引用次数: 0

Abstract

This study presents the numerical simulation of chaotic behavior in autonomous nonlinear dynamic models with fractional-order derivatives, aiming to analyze the effectiveness of different numerical methods in obtaining chaotic attractors. Six fractional-order chaotic oscillators are examined, applying the Grünwald–Letnikov definition approximations and the Adams–Bashforth–Moulton method using a predictor–corrector scheme. Equilibrium points are analyzed, and eigenvalues are calculated to determine the minimum order of derivatives that guarantees chaotic behavior. The results show significant differences between the methods in terms of accuracy and efficiency, highlighting the importance of selecting the numerical method in the simulation of fractional systems.

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应用gr nwald - letnikov定义和Adams-Bashforth-Moulton方法模拟分数阶混沌振子

本文对具有分数阶导数的自主非线性动力学模型的混沌行为进行了数值模拟，旨在分析不同数值方法在获得混沌吸引子方面的有效性。应用gr nwald - letnikov定义近似和采用预测校正方案的Adams-Bashforth-Moulton方法，研究了六个分数阶混沌振子。分析了平衡点，计算了特征值，以确定保证混沌行为的导数的最小阶数。结果表明，两种方法在精度和效率方面存在显著差异，突出了在分数系统模拟中选择数值方法的重要性。

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

Integration-The Vlsi Journal 工程技术-工程：电子与电气

CiteScore

3.80

自引率

5.30%

发文量

107

审稿时长

6 months

期刊介绍： Integration''s aim is to cover every aspect of the VLSI area, with an emphasis on cross-fertilization between various fields of science, and the design, verification, test and applications of integrated circuits and systems, as well as closely related topics in process and device technologies. Individual issues will feature peer-reviewed tutorials and articles as well as reviews of recent publications. The intended coverage of the journal can be assessed by examining the following (non-exclusive) list of topics: Specification methods and languages; Analog/Digital Integrated Circuits and Systems; VLSI architectures; Algorithms, methods and tools for modeling, simulation, synthesis and verification of integrated circuits and systems of any complexity; Embedded systems; High-level synthesis for VLSI systems; Logic synthesis and finite automata; Testing, design-for-test and test generation algorithms; Physical design; Formal verification; Algorithms implemented in VLSI systems; Systems engineering; Heterogeneous systems.