Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Jessica Zaqueros-Martinez, Gustavo Rodriguez-Gomez*, Esteban Tlelo-Cuautle, Felipe Orihuela-Espina

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

Original languageEnglish
Article number495
Number of pages23
JournalEntropy
Volume25
Issue number3
DOIs
Publication statusPublished - 13 Mar 2023

Keywords

  • Article
  • T–S fuzzy model
  • chaos
  • fuzzy control
  • hidden attractor
  • synchronization

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