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Based on third-order spiral chaotic Colpitts oscillator model, by introducing two piecewise-linear triangular function, a novel four-dimensional multi-scroll hyperchaotic system is constructed, which can generate （2M+1）×（2N+1）, （2M+1） and （2N+1）-scroll chaotic and hyperchaotic attractors. By using phase portrait, Poincaré mapping, Lyapunov exponent spectrum and bifurcation diagram, the dynamical behaviors of the proposed multi-scroll hyperchaotic system are analyzed. These results indicate that Hopf bifurcation point of multi-scroll hyperchaotic system is only related with the control parameter, but its scroll number and ranges of the control parameter for chaotic and hyperchaotic states increase along with the number of turning points. Furthermore, an analog circuit was designed to realize the four-dimensional multi-scroll hyperchaotic system. The results of experimental output and numerical simulation are basically the same.
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Keywords:
- multi-scroll hyperchaotic attractor /
- triangular function /
- equilibrium /
- circuit realization
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[2] ［2]Yalcin M 2007 Int. J. Bifur. Chaos 17 4471
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[4] ［4]Yalcin M, Mzoguz S 2007 Chaos 17 033112
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[6] ［6]Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[7] ［7]Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[8] ［8]Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234
[9] ［9]Lü J H, Yu S M, Leung H, Chen G R l 2006 IEEE Trans. Circuits Syst. I 53 149
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[11] ［11]Deng W H, Lü J H 2006 Chaos 16 043120
[12] ［12]Yu S M, Lin Q H, Qiu S S 2003 Acta Phys. Sin. 52 25 （in Chinese）［禹思敏、 林清华、 丘水生 2003 52 25］
[13] ［13]Yu S M, Lin Q H, Qiu S S 2004 Acta Phys. Sin. 53 2084 （in Chinese）［禹思敏、 林清华、 丘水生 2004 53 2084］
[14] ［14]Yu S M 2005 Acta Phys. Sin. 54 1500 （in Chinese）［禹思敏 2005 54 1500］
[15] ［15]Yu S M, Lü J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[16] ［16]Yu S M, Lü J H, Leung H, Chen G R 2005 IEEE Trans. Circuits Syst. I 52 1459
[17] ［17]Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 （in Chinese）［刘明华、 禹思敏 2006 55 5707］
[18] ［18]Yu S, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[19] ［19]Yu S M, Tang W K S, Lü J H, Chen G R 2008 Int. J. Circuit Theory and Appli. DOI: 101002/cta 558
[20] ［20]Radwan A, Soliman A, Elwakil A 2007 Int. J. Bifur. Chaos 17 227
[21] ［21]Gandhi G, Roska T 2008 Int. J. Circuit Theory and Appli. DOI: 101002/cta 487
[22] ［22]Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[23] ［23]Wang F Q, Liu C X 2006 Chin. Phys. 15 2878
[24] ［24]Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 （in Chinese）［王发强、刘崇新 2007 56 1983］
[25] ［25]Wang F Q, Liu C X, Lu J J 2006 Acta Phys. Sin. 55 3289 （in Chinese）［王发强、 刘崇新、 逯俊杰 2006 55 3289］
[26] ［26]Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 （in Chinese）［谌龙、 彭海军、 王德石2008 57 3337］
[27] ［27]Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 （in Chinese）［张朝霞、 禹思敏 2009 58 120］
[28] ［28]Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 （in Chinese）［罗小华、李华青、代祥光2008 57 7511］
[29] ［29]Maggio G M, Feo O D, Kennedy M P 1999 IEEE Trans. Circuits Syst. I 46 1118
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[1] ［1]Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[2] ［2]Yalcin M 2007 Int. J. Bifur. Chaos 17 4471
[3] ［3]Yalcin M, Suykens J, Vandewalle J, Ｍzoguz S 2002 Int. J. Bifur. Chaos 12 23
[4] ［4]Yalcin M, Mzoguz S 2007 Chaos 17 033112
[5] ［5]Lü J H, Yu X H, Chen G R 2003 IEEE Trans. Circuits Syst. I 50 198
[6] ［6]Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[7] ［7]Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[8] ［8]Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Physics Letters A 372 3234
[9] ［9]Lü J H, Yu S M, Leung H, Chen G R l 2006 IEEE Trans. Circuits Syst. I 53 149
[10] ［10]Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[11] ［11]Deng W H, Lü J H 2006 Chaos 16 043120
[12] ［12]Yu S M, Lin Q H, Qiu S S 2003 Acta Phys. Sin. 52 25 （in Chinese）［禹思敏、 林清华、 丘水生 2003 52 25］
[13] ［13]Yu S M, Lin Q H, Qiu S S 2004 Acta Phys. Sin. 53 2084 （in Chinese）［禹思敏、 林清华、 丘水生 2004 53 2084］
[14] ［14]Yu S M 2005 Acta Phys. Sin. 54 1500 （in Chinese）［禹思敏 2005 54 1500］
[15] ［15]Yu S M, Lü J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[16] ［16]Yu S M, Lü J H, Leung H, Chen G R 2005 IEEE Trans. Circuits Syst. I 52 1459
[17] ［17]Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 （in Chinese）［刘明华、 禹思敏 2006 55 5707］
[18] ［18]Yu S, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. II 55 1168
[19] ［19]Yu S M, Tang W K S, Lü J H, Chen G R 2008 Int. J. Circuit Theory and Appli. DOI: 101002/cta 558
[20] ［20]Radwan A, Soliman A, Elwakil A 2007 Int. J. Bifur. Chaos 17 227
[21] ［21]Gandhi G, Roska T 2008 Int. J. Circuit Theory and Appli. DOI: 101002/cta 487
[22] ［22]Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[23] ［23]Wang F Q, Liu C X 2006 Chin. Phys. 15 2878
[24] ［24]Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 （in Chinese）［王发强、刘崇新 2007 56 1983］
[25] ［25]Wang F Q, Liu C X, Lu J J 2006 Acta Phys. Sin. 55 3289 （in Chinese）［王发强、 刘崇新、 逯俊杰 2006 55 3289］
[26] ［26]Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 （in Chinese）［谌龙、 彭海军、 王德石2008 57 3337］
[27] ［27]Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 （in Chinese）［张朝霞、 禹思敏 2009 58 120］
[28] ［28]Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 （in Chinese）［罗小华、李华青、代祥光2008 57 7511］
[29] ［29]Maggio G M, Feo O D, Kennedy M P 1999 IEEE Trans. Circuits Syst. I 46 1118
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