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Comparison of synchronization of chaotic Burke-Shaw attractor with active control and integer-order and fractional-order P-C method

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  • Durdu, Ali
  • Uyaroğlu, Yılmaz

Abstract

Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure communication applications using synchronization methods are also presented in the literature. In the study, synchronization performances of two popular synchronization methods, active control and Pecaro Carroll (P-C) methods for secure communication application are compared. The Burke-Shaw chaotic attractor was synchronized with active control, integer-order and fractional-order P-C methods and their performances were compared. Both synchronization methods are modeled in Matlab™ environment. In both synchronization methods, it is shown with error graphs that the two systems are synchronized. Experimental results showed that the P-C method with optimal fractional value synchronized in 2.3 (time units) shorter than the active control method. The shortening of the synchronization time ensures that the synchronization is faster in secure communication applications, allowing the transmitted signal to reach the receiver faster from the sender. It shows that the P-C method with optimal fractional-order creates a lower delay in the synchronization time and is more suitable for use in secure communication applications. In addition, a secure communication application was made with the method proposed in the study and it was shown that the system could be used in secure communication applications.

Suggested Citation

  • Durdu, Ali & Uyaroğlu, Yılmaz, 2022. "Comparison of synchronization of chaotic Burke-Shaw attractor with active control and integer-order and fractional-order P-C method," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008256
    DOI: 10.1016/j.chaos.2022.112646
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    References listed on IDEAS

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    1. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    2. Uçar, Ahmet & Lonngren, Karl E. & Bai, Er-Wei, 2006. "Synchronization of the unified chaotic systems via active control," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1292-1297.
    3. Durdu, Ali & Uyaroğlu, Yılmaz, 2017. "The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 98-106.
    4. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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