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Through introducing two piecewise-linear functions into a three-dimensional linear system, a grid-scroll chaotic system with relatively simple algebraic of system structure is constructed. By deploying the zero points of the introduced saw-tooth function and modified saw-tooth function, the designs of the number and the distribution of the index-2 equilibrium points of the system are performed, and the controls of the scroll number and the scroll distribution of the chaotic attractor generated from the system are achieved. By using analog components such as operational amplifier, multiplier, etc., the saw-tooth function circuit, the modified saw-tooth function circuit and the three-dimensional linear system circuit are designed and the proposed grid-scroll chaotic system is implemented. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the designs of the scroll number and scroll distribution of chaotic attractors.
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Keywords:
- chaotic system /
- attractor /
- piecewise-linear function /
- circuit realization
[1] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits syst. I 40 861
[2] Yalcin M E 2007 Int. J. Bifur. Chaos 174471
[3] Yalcin M E, Suykens J, Vandewalle J, zoguz S 2002 Int. J. Bifur. Chaos 12 23
[4] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[5] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[6] Yu S M, Lü J H, Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087
[7] Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[8] Zhang C X, Yu S M 2009 Chin. Phys. B 18 119
[9] Gandhi G, Roska T 2009 Int. J. Circuit Theory and Appli. 37 473
[10] Bao B C, Zhou G H, Xu J P, Liu Z 2010 Int. J. Bifur. Chaos 20 2203
[11] Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成、刘 中、许建平、朱 雷 2010 物理学 报 59 1540]
[12] Xu Y M, Bao B C, Xu Q 2010 Acta Phys. Sin. 59 5959 (in Chinese) [徐煜明、包伯成、徐 强 2010 59 5959]
[13] Yu S M, Tang W K S, Lü J H, Chen G R 2010 Int. J. Circuit Theory and Appli. 38 243
[14] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[15] Yalcin M, zoguz S 2007 Chaos 17 033112
[16] Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234
[17] Mohamed I R, Murali K, Sinha S, Lindberg E 2010 Int. J. Bifur. Chaos 20 2185
[18] Zhang C X, Tang W K S, Yu S M 2009 Int. J. Bifur. Chaos 19 2073
[19] Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必、曾以成、徐茂林、陈家胜 2011 60 020507]
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[1] Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits syst. I 40 861
[2] Yalcin M E 2007 Int. J. Bifur. Chaos 174471
[3] Yalcin M E, Suykens J, Vandewalle J, zoguz S 2002 Int. J. Bifur. Chaos 12 23
[4] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[5] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[6] Yu S M, Lü J H, Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087
[7] Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[8] Zhang C X, Yu S M 2009 Chin. Phys. B 18 119
[9] Gandhi G, Roska T 2009 Int. J. Circuit Theory and Appli. 37 473
[10] Bao B C, Zhou G H, Xu J P, Liu Z 2010 Int. J. Bifur. Chaos 20 2203
[11] Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成、刘 中、许建平、朱 雷 2010 物理学 报 59 1540]
[12] Xu Y M, Bao B C, Xu Q 2010 Acta Phys. Sin. 59 5959 (in Chinese) [徐煜明、包伯成、徐 强 2010 59 5959]
[13] Yu S M, Tang W K S, Lü J H, Chen G R 2010 Int. J. Circuit Theory and Appli. 38 243
[14] Yu S M, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[15] Yalcin M, zoguz S 2007 Chaos 17 033112
[16] Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234
[17] Mohamed I R, Murali K, Sinha S, Lindberg E 2010 Int. J. Bifur. Chaos 20 2185
[18] Zhang C X, Tang W K S, Yu S M 2009 Int. J. Bifur. Chaos 19 2073
[19] Chen S B, Zeng Y C, Xu M L, Chen J S 2011 Acta Phys. Sin. 60 020507 (in Chinese) [陈仕必、曾以成、徐茂林、陈家胜 2011 60 020507]
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