Fractional-order projection of a chaotic system with hidden attractors and its passivity-based synchronization

Frontiers in Applied Mathematics and Statistics

Applied Mathematics and Statistics

Jesus M. Munoz-Pacheco¹  Marco A. Flores²  Fernando E. Serrano² 

[1] Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla (BUAP), Puebla, Mexico;Instituto de Investigación en Energía IIE, Universidad Nacional Autonoma de Honduras (UNAH), Tegucigalpa, Honduras;

关键词: chaotic system;    synchronization;    hidden attractor;    fractional-order;    passivity-based control;    chaos;   

DOI  :  10.3389/fams.2023.1267664

 received in 2023-07-26, accepted in 2023-09-05,  发布年份 2023

来源: Frontiers

【 摘 要 】

This paper presents the fractional-order projection of a chaotic system, which delivers a collection of self-excited and hidden chaotic attractors as a function of a single system parameter. Based on an integer-order chaotic system and the proposed transformation, the fractional-order chaotic system obtains when the divergence of integer and fractional vector fields flows in the same direction. Phase portraits, bifurcation diagrams, and Lyapunov exponents validate the chaos generation. Apart from these results, two passivity-based fractional control laws are designed effectively for the integer and fractional-order chaotic systems. In both cases, the synchronization schemes depend on suitable storage functions given by the fractional Lyapunov theory. Several numerical experiments confirm the proposed approach and agree well with the mathematical deductions.

【 授权许可】

Unknown   
Copyright © 2023 Serrano, Munoz-Pacheco and Flores.