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Synchronization and anti-synchronization for chaotic systems

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  • Song, Qiankun
  • Cao, Jinde

Abstract

Based on a suitable separation method, combined with the Lyapunov stability and the matrix measure theory, the complete synchronization and anti-synchronization for chaotic systems are investigated. Several sufficient conditions and some necessary and sufficient conditions are obtained respectively. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results, since an adjustable non-singular matrix is given. They are of great significance in the design and applications of synchronization and anti-synchronization of chaotic systems. Two examples are given to show the effectiveness of the proposed method.

Suggested Citation

  • Song, Qiankun & Cao, Jinde, 2007. "Synchronization and anti-synchronization for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 929-939.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:3:p:929-939
    DOI: 10.1016/j.chaos.2006.01.041
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    References listed on IDEAS

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    1. Liu, Bin & Chen, Guanrong & Teo, Kok Lay & Liu, Xinzhi, 2005. "Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1629-1641.
    2. Cao, Jinde & Li, H.X. & Ho, Daniel W.C., 2005. "Synchronization criteria of Lur’e systems with time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1285-1298.
    3. Cheng, Chao-Jung & Liao, Teh-Lu & Hwang, Chi-Chuan, 2005. "Exponential synchronization of a class of chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 197-206.
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    Cited by:

    1. Priyanka, K. Sri Raja & Soundararajan, G. & Kashkynbayev, Ardak & Nagamani, G., 2023. "Exponential H∞ synchronization and anti-synchronization of delayed discrete-time complex-valued neural networks with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 301-321.
    2. Israr Ahmad & Azizan Bin Saaban & Adyda Binti Ibrahim & Mohammad Shahzad, 2015. "Robust Finite-Time Anti-Synchronization of Chaotic Systems with Different Dimensions," Mathematics, MDPI, vol. 3(4), pages 1-19, December.
    3. Zhang, Yinping & Sun, Jitao, 2009. "Robust synchronization of coupled delayed neural networks under general impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1476-1480.
    4. He, Guangming & Yang, Jingyu, 2008. "Adaptive synchronization in nonlinearly coupled dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1254-1259.

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