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Based on the microcontroller (MCU), a universal digital hardware experimental circuit for four-dimensional chaotic system is designed, from which 9×7-grids scroll chaotic and hyperchaotic attractors are generated. Reference [1] has presented a four-dimensional multi-scroll hyperchaotic system extended from Colpitts oscillator model. In this paper, a new four-dimensional grid-scroll hyperchaotic system is constructed by introducing a unit sawtooth wave function to replace the triangular function in the original system, which is realized by utilizing MCU digital hardware implementation easily. Analysis and numerical simulations are performed for the formation mechanism of grid-scroll attractor in the new system. By using Euler algorithm to discretize the proposed grid-scroll hyperchaotic system, an attractor with more grid-scroll number than that of the original system can be generated in the effective dynamic range of the experimental circuit. Experimental results verified the feasibility of grid-scroll hyperchaotic system based on MCU implementation.
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Keywords:
- grid-scroll hyperchaotic system /
- unit sawtooth wave function /
- microcontroller (MCU) /
- digital hardware implementation
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[2] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
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[6] 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]
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[10] Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 54 1500]
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[12] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. Ⅰ 53 149
[13] Yu S, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. Ⅱ 55 1168
[14] Deng W H, Lü J H 2007 Phys. Lett. A 369 438
[15] Yalcin M, zoguz S 2007 Chaos 17 033112
[16] Deng W H, Lü J H 2006 Chaos 16 043120
[17] 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]
[18] Yu S M, Lü J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[19] Radwan A, Soliman A, Elwakil A 2007 Int. J. Bifur. Chaos 17 227
[20] Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[21] Wang F Q, Liu C X 2006 Chin. Phys. 15 2878
[22] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 56 1983]
[23] 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]
[24] 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]
[25] Maggio G M, Feo O D, Kennedy M P 1999 IEEE Trans. Circuits Syst. Ⅰ 46 1118
[26] Zhou W J, Yu S M 2008 Acta Phys. Sin. 57 4738 (in Chinese) [周武杰、禹思敏 2008 57 4738]
[27] Yu S M, Lü J H 2007 Proc. 26th Chinese Control Conf. (Vol. 6)(Beijing: Beijing Uni. of Aeronautics and Astronautics Press) P409 (in Chinese) [禹思敏、吕金虎 2007 第26届中国控制会议论文集(第六卷)(北京:北京航空航天大学出版社)第409页]
[28] Zhang Z, Chen G R, Yu S M 2009 Int. J. Circ. Theor. Appl. 37 31
[29] Zhang Y, Yu S M, Liu M H 2007 J. Circ. and Syst. 12 39 (in Chinese) [张 钰、禹思敏、刘明华 2007 电路与系统学报 12 39]
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[1] Yalcin M E 2007 Int. J. Bifur. Chaos 17 4471
[2] Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[3] Zhou W J, Yu S M 2009 Acta Phys. Sin. 58 113 (in Chinese) [周武杰、禹思敏 2009 58 113]
[4] Bao B C, Liu Z, Xu J P, Zhu L 2010 Acta Phys. Sin. 59 1546 (in Chinese) [包伯成、刘 中、许建平、朱 雷 2010 59 1546]
[5] 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]
[6] 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]
[7] Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese)[张朝霞、禹思敏 2009 58 120]
[8] Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui MA 2008 Phys. Lett. A 372 3234
[9] Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 55 5707]
[10] Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 54 1500]
[11] Yu S M, Lü J H, Leung H, Chen G R 2005 IEEE Trans. Circuits Syst. Ⅰ 52 1459
[12] Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. Ⅰ 53 149
[13] Yu S, Tang W K S, Lü J H, Chen G R 2008 IEEE Trans. Circuits Syst. Ⅱ 55 1168
[14] Deng W H, Lü J H 2007 Phys. Lett. A 369 438
[15] Yalcin M, zoguz S 2007 Chaos 17 033112
[16] Deng W H, Lü J H 2006 Chaos 16 043120
[17] 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]
[18] Yu S M, Lü J H, Tang W K S, Chen G R 2006 Chaos 16 033126
[19] Radwan A, Soliman A, Elwakil A 2007 Int. J. Bifur. Chaos 17 227
[20] Wang F Q, Liu C X 2007 Chin. Phys. 16 942
[21] Wang F Q, Liu C X 2006 Chin. Phys. 15 2878
[22] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 56 1983]
[23] 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]
[24] 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]
[25] Maggio G M, Feo O D, Kennedy M P 1999 IEEE Trans. Circuits Syst. Ⅰ 46 1118
[26] Zhou W J, Yu S M 2008 Acta Phys. Sin. 57 4738 (in Chinese) [周武杰、禹思敏 2008 57 4738]
[27] Yu S M, Lü J H 2007 Proc. 26th Chinese Control Conf. (Vol. 6)(Beijing: Beijing Uni. of Aeronautics and Astronautics Press) P409 (in Chinese) [禹思敏、吕金虎 2007 第26届中国控制会议论文集(第六卷)(北京:北京航空航天大学出版社)第409页]
[28] Zhang Z, Chen G R, Yu S M 2009 Int. J. Circ. Theor. Appl. 37 31
[29] Zhang Y, Yu S M, Liu M H 2007 J. Circ. and Syst. 12 39 (in Chinese) [张 钰、禹思敏、刘明华 2007 电路与系统学报 12 39]
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