Fuzzy Synchronization of Chaotic Systems with Hidden Attractors
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 pres...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/3/495 |
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| author | Jessica Zaqueros-Martinez Gustavo Rodriguez-Gomez Esteban Tlelo-Cuautle Felipe Orihuela-Espina |
| author_facet | Jessica Zaqueros-Martinez Gustavo Rodriguez-Gomez Esteban Tlelo-Cuautle Felipe Orihuela-Espina |
| author_sort | Jessica Zaqueros-Martinez |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:34:33Z |
| format | Article |
| id | doaj.art-09ad5ab4ce1f4c5893f21a4d18bee710 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T06:34:33Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-09ad5ab4ce1f4c5893f21a4d18bee7102023-11-17T10:56:59ZengMDPI AGEntropy1099-43002023-03-0125349510.3390/e25030495Fuzzy Synchronization of Chaotic Systems with Hidden AttractorsJessica Zaqueros-Martinez0Gustavo Rodriguez-Gomez1Esteban Tlelo-Cuautle2Felipe Orihuela-Espina3Department of Computer Science, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla, Puebla 72840, MexicoDepartment of Computer Science, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla, Puebla 72840, MexicoDepartment of Electronics, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla, Puebla 72840, MexicoDepartment of Computer Science, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintla, Puebla 72840, MexicoChaotic 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.https://www.mdpi.com/1099-4300/25/3/495synchronizationchaoshidden attractorfuzzy controlT–S fuzzy model |
| spellingShingle | Jessica Zaqueros-Martinez Gustavo Rodriguez-Gomez Esteban Tlelo-Cuautle Felipe Orihuela-Espina Fuzzy Synchronization of Chaotic Systems with Hidden Attractors Entropy synchronization chaos hidden attractor fuzzy control T–S fuzzy model |
| title | Fuzzy Synchronization of Chaotic Systems with Hidden Attractors |
| title_full | Fuzzy Synchronization of Chaotic Systems with Hidden Attractors |
| title_fullStr | Fuzzy Synchronization of Chaotic Systems with Hidden Attractors |
| title_full_unstemmed | Fuzzy Synchronization of Chaotic Systems with Hidden Attractors |
| title_short | Fuzzy Synchronization of Chaotic Systems with Hidden Attractors |
| title_sort | fuzzy synchronization of chaotic systems with hidden attractors |
| topic | synchronization chaos hidden attractor fuzzy control T–S fuzzy model |
| url | https://www.mdpi.com/1099-4300/25/3/495 |
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