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In order to improve the complexity of chaotic signals, a new fractional-order four-dimensional hyperchaotic system is presented. Some dynamical properties of the system are investigated. The circuit implementation of this new system is simulated using Multisim. The results prove that chaos actually exists in the system with order as low as 3.2. A simple linear feedback controller is designed, and the simulation results are presented to demonstrate the effectiveness of the method.
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Keywords:
- fractional-order hyperchaotic system /
- dynamical property /
- circuit simulation /
- feedback controller
[1] Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957(in Chinese) [张若洵、杨世平 2009 58 2957]
[2] Lu J G 2006 Phys. Lett. A 354 305
[3] Zhou P, Cheng X F, Zhang N Y 2008 Acta Phys. Sin. 57 5407(in Chinese) [周 平、程雪峰、张年英 2008 59 5407]
[4] Li G L, Chen X Y 2010 Chin. Phys. B 19 030507
[5] Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese) [许 喆、刘崇新、杨 韬 2010 59 1524]
[6] Liu C X 2007 Chaos, Solitons and Fractals 4 25
[7] Gao T G, Chen G R, Chen Z Q 2007 Phys. lett. A 361 78
[8] Wei W, Li D H, Wang J 2010 Chin. Phys. B 19 040507
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549(in Chinese) [张若洵、杨世平、刘永利 2010 59 1549]
[10] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305(in Chinese) [赵灵冬、胡建兵、刘旭辉 2010 59 2305]
[11] Liu C X 2007 Acta Phys. Sin. 56 6865(in Chinese) [刘崇新 2007 56 6865]
[12] Xiao Y Z, Xu W, Li X C, Tang S F 2008 Chin. Phys. B 17 80
[13] Zhang Q J, Lu J A 2008 Chin. Phys. B 17 492
[14] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[15] Zhang X F, Fan J L 2010 Acta Phys. Sin. 59 2298(in Chinese) [张雪锋、范九伦 2010 59 2298]
[16] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[17] Jia H Y, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 4469(in Chinese) [贾红艳、陈增强、袁著祉 2009 58 4469]
[18] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[19] Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[20] Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255(in Chinese) [李春彪、陈 谡、朱焕强 2009 58 2255]
[21] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩 焱、赵灵冬 2009 58 4402]
[22] Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[23] Zhou P, Cheng X F, Zhang N Y 2008 Chin. Phys. B 17 3252
[24] Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
[25] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese) [陈向荣、刘崇新、王发强、李永勋 2008 57 1416]
[26] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456(in Chinese) [闵富红、余 杨、葛曹君 2009 58 1456]
[27] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p4
[28] Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[29] Matignon D 1996 IMACS, IEEE-SMC, Lille, France 963
[30] Ahmed E, El2Sayed A M A, Elsaka H A A 2007 J. Math. Anal. Appl. 325 542
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[1] Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957(in Chinese) [张若洵、杨世平 2009 58 2957]
[2] Lu J G 2006 Phys. Lett. A 354 305
[3] Zhou P, Cheng X F, Zhang N Y 2008 Acta Phys. Sin. 57 5407(in Chinese) [周 平、程雪峰、张年英 2008 59 5407]
[4] Li G L, Chen X Y 2010 Chin. Phys. B 19 030507
[5] Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese) [许 喆、刘崇新、杨 韬 2010 59 1524]
[6] Liu C X 2007 Chaos, Solitons and Fractals 4 25
[7] Gao T G, Chen G R, Chen Z Q 2007 Phys. lett. A 361 78
[8] Wei W, Li D H, Wang J 2010 Chin. Phys. B 19 040507
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549(in Chinese) [张若洵、杨世平、刘永利 2010 59 1549]
[10] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305(in Chinese) [赵灵冬、胡建兵、刘旭辉 2010 59 2305]
[11] Liu C X 2007 Acta Phys. Sin. 56 6865(in Chinese) [刘崇新 2007 56 6865]
[12] Xiao Y Z, Xu W, Li X C, Tang S F 2008 Chin. Phys. B 17 80
[13] Zhang Q J, Lu J A 2008 Chin. Phys. B 17 492
[14] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[15] Zhang X F, Fan J L 2010 Acta Phys. Sin. 59 2298(in Chinese) [张雪锋、范九伦 2010 59 2298]
[16] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[17] Jia H Y, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 4469(in Chinese) [贾红艳、陈增强、袁著祉 2009 58 4469]
[18] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[19] Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[20] Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255(in Chinese) [李春彪、陈 谡、朱焕强 2009 58 2255]
[21] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩 焱、赵灵冬 2009 58 4402]
[22] Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[23] Zhou P, Cheng X F, Zhang N Y 2008 Chin. Phys. B 17 3252
[24] Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
[25] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese) [陈向荣、刘崇新、王发强、李永勋 2008 57 1416]
[26] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456(in Chinese) [闵富红、余 杨、葛曹君 2009 58 1456]
[27] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p4
[28] Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[29] Matignon D 1996 IMACS, IEEE-SMC, Lille, France 963
[30] Ahmed E, El2Sayed A M A, Elsaka H A A 2007 J. Math. Anal. Appl. 325 542
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