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

被引：0

作者：

Silva-Juarez, Alejandro ^{[1
]}

Rosales-Nunez, Sergio A. ^{[2
]}

Alvarez-Simon, Luis C. ^{[2
,3
]}

Zamora-Mejia, Gregorio ^{[2
,3
]}

Carbajal-Gomez, Victor H. ^{[2
,3
]}

Bautista-Castillo, Alejandro I. ^{[2
]}

Rocha-Perez, Jose M. ^{[2
,4
]}

机构：

[1] Univ Tecnol Puebla, Div Mantenimiento Ind, Antiguo Camino Resurrecc 1002-A, Puebla 72300, Mexico

[2] Inst Nacl Astrofis Opt & Electr, Dept Sistemas & Circuitos Integrados SICI, Luis Enr Erro 1,Tonantzintla, Puebla 72840, Mexico

[3] Consejo Nacl Human Ciencia & Tecnol Conahcyt, Mexico City 03940, Mexico

[4] Benemerita Univ Autonoma Puebla BUAP, Fac Ciencias Elect, Puebla 72570, Mexico

来源：

INTEGRATION-THE VLSI JOURNAL | 2025年 / 102卷

关键词：

Fractional calculus; Numerical methods; Chaos; Gr & uuml; nwald-Letnikov; Adams-Bashforth-Moulton; Simulation; NUMERICAL-SOLUTION; ATTRACTORS;

D O I：

10.1016/j.vlsi.2025.102366

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 Gr & uuml;nwald- 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.

引用

页数：10

共 35 条

[1]

Baleanu D., 2011, Fractional dynamics and control

[2] On the simplest fractional-order memristor-based chaotic system [J].

Cafagna, Donato ;

Grassi, Giuseppe .

NONLINEAR DYNAMICS, 2012, 70 (02) :1185-1197

[3]

Canton E.C., 2023, Generation of Self-Excited, Hidden and Non-Self-Excited Attractors in Piecewise Linear Systems: Some Recent Approaches

[4] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[5] A Piecewise Linear Approach for Implementing Fractional-Order Multi-Scroll Chaotic Systems on ARMs and FPGAs [J].

Clemente-Lopez, Daniel ;

Munoz-Pacheco, Jesus M. ;

Zambrano-Serrano, Ernesto ;

Beltran, Olga G. Felix ;

Rangel-Magdaleno, Jose de Jesus .

FRACTAL AND FRACTIONAL, 2024, 8 (07)

[6] FPGA-based implementation of different families of fractional-order chaotic oscillators applying Grunwald-Letnikov method [J].

Dalia Pano-Azucena, Ana ;

Ovilla-Martinez, Brisbane ;

Tlelo-Cuautle, Esteban ;

Manuel Munoz-Pacheco, Jesus ;

Gerardo de la Fraga, Luis .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 72 :516-527

[7] Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system [J].

Deng, Weihua ;

Lu, Jinhu .

PHYSICS LETTERS A, 2007, 369 (5-6) :438-443

[8] A predictor-corrector approach for the numerical solution of fractional differential equations [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :3-22

[9]

Diethelm K., 1999, Forsch. Und Wiss. Rechn., V1998, P57

[10]

Dorcak L., 1994, P 11 INT C PROC CONT, P19

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