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Fuzzy Synchronization of Chaotic Systems with Hidden Attractors
Jessica Zaqueros-Martinez1, Gustavo Rodriguez-Gomez1, Esteban Tlelo-Cuautle2
1Department of Computer Science, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla, Puebla 72840, Mexico.
Entropy (Basel, Switzerland)
|March 29, 2023
Summary
Fuzzy control effectively synchronizes chaotic systems with hidden attractors using a specialized numerical integration method. This approach enhances synchronization performance and offers optimized error convergence for projective synchronization.
Area of Science:
- Chaos theory
- Control systems engineering
- Computational mathematics
Background:
- Synchronizing chaotic systems is challenging, especially those with hidden attractors.
- Control strategy selection is critical and must account for system-specific features like hidden attractors.
Purpose of the Study:
- To investigate the efficacy of fuzzy control for synchronizing chaotic systems with hidden attractors.
- To develop and test a specialized numerical integration method tailored for chaotic system oscillations.
Main Methods:
- Utilized fuzzy control strategies for complete and projective synchronization.
- Employed a novel numerical integration technique exploiting chaotic system oscillatory characteristics.
- Applied tensor product (TP) model transformation to generate Takagi-Sugeno (T-S) fuzzy models.
- Proposed an optimization strategy for error convergence in projective synchronization.
Main Results:
- Fuzzy control combined with the specialized numerical integration method proved effective for synchronizing chaotic systems with hidden attractors.
- The choice of fuzzy model significantly impacted synchronization performance.
- An effective strategy for optimizing error convergence in projective synchronization was developed.
Conclusions:
- Fuzzy control and the specialized numerical integration method offer a viable solution for synchronizing chaotic systems with hidden attractors.
- The study highlights the influence of fuzzy model selection on synchronization outcomes.
- The proposed methods advance the field of chaotic system control and synchronization.
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