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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.
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.
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