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Taking Chua's circuit with a smooth cubic flux-controlled memristor as an example, the impulsive control synchronization method for two identical memristor-based chaotic systems is studied. Based on the Lyapunov stability theory, the asymptotic stability condition for the impulsive synchronization of the memristor-based chaotic systems is given. Combining with the maximum conditional Lyapunov exponent spectrum of the error system, effects of the system initial values on the performances of impulsive synchronization are discussed, and corresponding simulation experiments are performed. Results indicate that using impulsive synchronization for the two identical memristor-based chaotic systems is feasible and effective with appropriate impulsive control parameters; the initial values of the memristor-based chaotic systems have some effects on the performances of impulsive synchronization, which can be inhibited by increasing the impulsive coupling strength.
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Keywords:
- impulsive synchronization /
- Lyapunov function /
- memristor-based chaotic system /
- initial values
[1] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[2] Bao B C, Xu J P, Liu Z 2010 Chin. Phys. Lett. 27 070504
[3] Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 59 3785]
[4] Yang F Y, Leng J L, Li Q D 2014 Acta Phys. Sin. 63 080502 (in Chinese) [杨芳艳, 冷家丽, 李清都 2014 63 080502]
[5] Wang G Y, He J L, Yuan F, Peng C J 2013 Chin. Phys. Lett. 30 110506
[6] Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[7] Bao B C, Zou X, Liu Z, Hu F W 2013 Int. J. Bifurc. Chaos 23 1350135
[8] Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 63 010502]
[9] Wang B X, Jian J G, Yu H 2014 Syst. Sci. and Control Eng.: An Open Access J. 2 291
[10] El-Sayed A M A, Elsaid A, Nour H M, Elsonbaty A 2013 Commun. Nonlin. Sci. Numer. Simul. 18 148
[11] Wen S P, Zeng Z G, Huang T W, Chen Y R 2013 Phys. Lett. A 377 2016
[12] Liu Z, Chen S Y, Xi F 2012 Int. J. Bifurc. Chaos 22 1250151
[13] Xi F, Chen S Y, Liu Z 2013 Int. J. Bifurc. Chaos 23 1350198
[14] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[15] Pyragas K 1993 Phys. Lett. A 181 203
[16] Huang D 2005 Phys. Rev. E 71 037203
[17] Yang T, Chua L O 1997 IEEE Trans. Circuits Syst. I: Fund. Theor. and Appl. 44 976
[18] Liu D F, Wu Z Y, Ye Q L 2014 Nonlin. Dyn. 75 209
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[1] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[2] Bao B C, Xu J P, Liu Z 2010 Chin. Phys. Lett. 27 070504
[3] Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 59 3785]
[4] Yang F Y, Leng J L, Li Q D 2014 Acta Phys. Sin. 63 080502 (in Chinese) [杨芳艳, 冷家丽, 李清都 2014 63 080502]
[5] Wang G Y, He J L, Yuan F, Peng C J 2013 Chin. Phys. Lett. 30 110506
[6] Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[7] Bao B C, Zou X, Liu Z, Hu F W 2013 Int. J. Bifurc. Chaos 23 1350135
[8] Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 63 010502]
[9] Wang B X, Jian J G, Yu H 2014 Syst. Sci. and Control Eng.: An Open Access J. 2 291
[10] El-Sayed A M A, Elsaid A, Nour H M, Elsonbaty A 2013 Commun. Nonlin. Sci. Numer. Simul. 18 148
[11] Wen S P, Zeng Z G, Huang T W, Chen Y R 2013 Phys. Lett. A 377 2016
[12] Liu Z, Chen S Y, Xi F 2012 Int. J. Bifurc. Chaos 22 1250151
[13] Xi F, Chen S Y, Liu Z 2013 Int. J. Bifurc. Chaos 23 1350198
[14] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[15] Pyragas K 1993 Phys. Lett. A 181 203
[16] Huang D 2005 Phys. Rev. E 71 037203
[17] Yang T, Chua L O 1997 IEEE Trans. Circuits Syst. I: Fund. Theor. and Appl. 44 976
[18] Liu D F, Wu Z Y, Ye Q L 2014 Nonlin. Dyn. 75 209
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