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

被引：3
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.
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页数：10
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