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In this paper, we primarily investigate the adaptive modifying function projective synchronization of a class of chaotic systems with uncertainties. According to the Lyapunov stability theory, the two schemes of obtaining the response system from chaotic system are established, and the controller and the adaptive law are designed. The approach is more robust to noise and external interference, and does not need the upper bound of uncertainties in advance. In addition, it can adjust the system response rapidly by adjusting the accelerated factor. This method is more practical. Numerical simulations of a hyper-chaotic system verify the effectiveness of the proposed method.
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Keywords:
- chaotic systems /
- modified function projective synchronization /
- adaptive control /
- acclerated factor
[1] Du H Y 2009 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [杜洪越 2009 博士学位论文 (哈尔滨:哈尔滨工业大学)]
[2] Li Z, Xu D 2004 Chaos, Solitons and Fractals 22 477
[3] Chee C Y, Xu D 2005 Chaos, Solitons and Fractals 23 1063
[4] Hu M F, Xu Z Y 2008 Nonlinear Analysis RWA. 9 1253
[5] Li J F, Li N, Liu Y P 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农, 刘宇平 2011 60 080507]
[6] Du H, Zeng Q, Wong C 2009 Chaos, Solitons and Fractals 42 2399
[7] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[8] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2264 (in Chinese) [王建安, 刘贺平 2010 59 2264]
[9] Sun K H, Qiu S S, Yin L Z 2010 Information and Control 39 326 (in Chinese) [孙克辉, 丘水生, 尹林子 2010 信息与控制 39 326]
[10] Wang J A, Li Z J, Liu H P 2010 Systems Engineering and Electronics 32 1745 (in Chinese) [王健安, 李壮举, 刘贺平 2010 系统工程与电子技术 32 1745]
[11] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[12] Luo R Z, Wei Z M 2009 Chaos, Solitons and Fractals 42 1266
[13] Yu Y G, Li H X 2010 Nonlinear Analysis: Real World Applications 11 2456
[14] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 3743
[15] Zheng S, Dong G G, Bi Q S 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3547
[16] Yang X K, Cai L, Zhao X H, Feng C W 2010 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 59 3740]
[17] Li H Q, Liao X F, Huang H Y 2011 Acta Phys. Sin. 60 020512 (in Chinese) [李华青, 廖晓峰, 黄宏宇 2011 60 020512]
[18] Lin J S, Yan J J, Liao T L 2005 Chaos, Solitons and Fractals 24 371
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[1] Du H Y 2009 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [杜洪越 2009 博士学位论文 (哈尔滨:哈尔滨工业大学)]
[2] Li Z, Xu D 2004 Chaos, Solitons and Fractals 22 477
[3] Chee C Y, Xu D 2005 Chaos, Solitons and Fractals 23 1063
[4] Hu M F, Xu Z Y 2008 Nonlinear Analysis RWA. 9 1253
[5] Li J F, Li N, Liu Y P 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农, 刘宇平 2011 60 080507]
[6] Du H, Zeng Q, Wong C 2009 Chaos, Solitons and Fractals 42 2399
[7] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[8] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2264 (in Chinese) [王建安, 刘贺平 2010 59 2264]
[9] Sun K H, Qiu S S, Yin L Z 2010 Information and Control 39 326 (in Chinese) [孙克辉, 丘水生, 尹林子 2010 信息与控制 39 326]
[10] Wang J A, Li Z J, Liu H P 2010 Systems Engineering and Electronics 32 1745 (in Chinese) [王健安, 李壮举, 刘贺平 2010 系统工程与电子技术 32 1745]
[11] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[12] Luo R Z, Wei Z M 2009 Chaos, Solitons and Fractals 42 1266
[13] Yu Y G, Li H X 2010 Nonlinear Analysis: Real World Applications 11 2456
[14] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 3743
[15] Zheng S, Dong G G, Bi Q S 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3547
[16] Yang X K, Cai L, Zhao X H, Feng C W 2010 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 59 3740]
[17] Li H Q, Liao X F, Huang H Y 2011 Acta Phys. Sin. 60 020512 (in Chinese) [李华青, 廖晓峰, 黄宏宇 2011 60 020512]
[18] Lin J S, Yan J J, Liao T L 2005 Chaos, Solitons and Fractals 24 371
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