Poincaré maps for detecting chaos in fractional-order systems with hidden attractors for its Kaplan-Yorke dimension optimization

AIMS Mathematics

卷:7

Esteban Tlelo-Cuautle¹  Daniel Clemente-López¹  José de Jesús Rangel-Magdaleno¹  Luis-Gerardo de la Fraga²  Jesus Manuel Munoz-Pacheco³ 

[1] 1. Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Luis Enrique Erro No. 1, Tonantzintla, Puebla 72840, Mexico;

[2] 2. Computer Science Department, Cinvestav, Av. IPN 2508, Mexico City 07360, Mexico;

[3] 3. Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, 18 Sur y Avenida San Claudio San Manuel, Puebla 72592, Mexico;

关键词: chaos;    fractional calculus;    poincarémap;    differential evolution algorithm;    accelerated particle swarm optimization;    kaplan-yorke dimension;   

DOI  :  10.3934/math.2022326

来源: DOAJ

【 摘 要 】

The optimization of fractional-order (FO) chaotic systems is challenging when simulating a considerable number of cases for long times, where the primary problem is verifying if the given parameter values will generate chaotic behavior. In this manner, we introduce a methodology for detecting chaotic behavior in FO systems through the analysis of Poincaré maps. The optimization process is performed applying differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms for maximizing the Kaplan-Yorke dimension (DKY) of two case studies: a 3D and a 4D FO chaotic systems with hidden attractors. These FO chaotic systems are solved applying the Grünwald-Letnikov method, and the Numba just-in-time (jit) compiler is used to improve the optimization process's time execution in Python programming language. The optimization results show that the proposed method efficiently optimizes FO chaotic systems with hidden attractors while saving execution time.

【 授权许可】

Unknown