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Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique.

Jesus M Munoz-Pacheco¹, Christos Volos², Fernando E Serrano³

¹Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico.

Entropy (Basel, Switzerland)

|August 6, 2021

Summary

This study demonstrates the stabilization and synchronization of a complex hidden chaotic attractor using a complex Lorenz system. A backstepping controller was developed to achieve synchronization, enhancing control strategies for chaotic systems.

Keywords:

backstepping controller chaotic systems hidden attractors stabilization synchronization

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Area of Science:

Nonlinear Dynamics
Chaos Theory
Control Systems Engineering

Background:

Complex Lorenz systems exhibit intricate chaotic behaviors.
Hidden chaotic attractors are challenging to find and control.
Understanding vector field properties is crucial for dynamic analysis.

Purpose of the Study:

To analyze the dynamics of a complex Lorenz chaotic system.
To discover a hidden chaotic attractor by manipulating system parameters.
To achieve stabilization and synchronization of the identified chaotic attractor.

Main Methods:

Dynamic analysis of the complex Lorenz system in the Cn domain.
Utilizing set topology to find the intersection of sets for hidden attractor discovery.
Deriving a backstepping controller using recursive methodology and Lyapunov functionals.
Implementing a control synchronization law based on error variables.

Main Results:

Successfully identified a hidden chaotic attractor within the complex Lorenz system.
Developed and applied a backstepping controller for system stabilization.
Achieved synchronization of a response system with the original complex Lorenz system.

Conclusions:

The proposed backstepping controller effectively stabilizes and synchronizes the complex hidden chaotic attractor.
This research provides a novel method for discovering and controlling hidden chaotic attractors.
The findings contribute to advancements in nonlinear dynamics and control theory.