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Firstly, a new fractional-order chaotic system is proposed. When the linear term x in the second formula of the system was replaced by its absolute value, the range of its unique parameter k that makes the wing of the original system doubled is explored in detail. Furthermore, the numerical simulation and the circuit simulation of the original system and its double-wing system are achieved via Matlab and Multisim software respectively. Finally, based on sliding mode control theory and stability theory in fractional calculus, a new sliding mode controller is designed to realize the synchronization of the new system and its double-wing system respectively. Simulation results are provided to illustrate the effectiveness of the proposed scheme.
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Keywords:
- fractional-order /
- double-wing /
- sliding mode control /
- synchronization
[1] Ross B 1977 Hist. Math. 4 75
[2] Elwakil S A, Zahran M A 1999 Chaos, Solitons & Fractals 10 1545
[3] Herrmann R 2010 Physica A 389 4613
[4] Li C L, Yu S M, Luo X S 2012 Chin. Phys. B 21 100506
[5] Cafagna D, Grassi G 2008 Int. J. Bifurc. Chaos 18 1845
[6] Petras I 2010 IEEE Trans. Circuits Syst. II, Express Briefs 57 975
[7] Lu J G 2006 Phys. Lett. A 354 305
[8] Xu Z, Liu C X 2008 Chin. Phys. B 17 4033
[9] Jia H Y, Chen Z Q, Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [贾红艳, 陈增强, 薛薇 2013 62 140503]
[10] Chen D Y, Liu C F, Wu C, Liu Y J, Ma X Y, You Y J 2012 Circuits Syst. Signal Process. 31 1599
[11] Liu F, Ren Y, Shan X M, Qiu Z L 2002 Chaos, Solitons & Fractals 13 723
[12] Arman K, Kia F, Naser P, Henry L 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[13] Zhou P, Ding R 2012 Mathematical Problems in Engineering doi:10.1155/2012/214169
[14] Chen Z W, Wang J, Pang S J 2012 Acta Phys. Sin. 61 220505 (in Chinese) [陈志旺, 王敬, 庞双杰 2012 61 220505]
[15] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[16] Zhang R X, Yang S P 2012 Chin. Phys. B 21 030505
[17] Liu J G 2013 Chin. Phys. B 22 060510
[18] Zhou P, Ding R, Cao Y X 2012 Nonlinear Dyn. 70 1263
[19] Li T, Yu J J, Wang Z 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1796
[20] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强, 刘崇新 2006 55 5055]
[21] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 62 080507]
[22] Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[23] Li G H 2004 Acta Phys. Sin. 53 999 (in Chinese) [李国辉 2004 53 999]
[24] Zhou P, Zhu W 2011 Nonlinear Analysis: Real World Applications 12 811
[25] Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 61 160510]
[26] Chen D Y, Zhang R F, Ma X Y, Wang J 2012 Chin. Phys. B 21 120507
[27] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese) [王发强, 刘崇新 2006 55 3922]
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[1] Ross B 1977 Hist. Math. 4 75
[2] Elwakil S A, Zahran M A 1999 Chaos, Solitons & Fractals 10 1545
[3] Herrmann R 2010 Physica A 389 4613
[4] Li C L, Yu S M, Luo X S 2012 Chin. Phys. B 21 100506
[5] Cafagna D, Grassi G 2008 Int. J. Bifurc. Chaos 18 1845
[6] Petras I 2010 IEEE Trans. Circuits Syst. II, Express Briefs 57 975
[7] Lu J G 2006 Phys. Lett. A 354 305
[8] Xu Z, Liu C X 2008 Chin. Phys. B 17 4033
[9] Jia H Y, Chen Z Q, Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [贾红艳, 陈增强, 薛薇 2013 62 140503]
[10] Chen D Y, Liu C F, Wu C, Liu Y J, Ma X Y, You Y J 2012 Circuits Syst. Signal Process. 31 1599
[11] Liu F, Ren Y, Shan X M, Qiu Z L 2002 Chaos, Solitons & Fractals 13 723
[12] Arman K, Kia F, Naser P, Henry L 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[13] Zhou P, Ding R 2012 Mathematical Problems in Engineering doi:10.1155/2012/214169
[14] Chen Z W, Wang J, Pang S J 2012 Acta Phys. Sin. 61 220505 (in Chinese) [陈志旺, 王敬, 庞双杰 2012 61 220505]
[15] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[16] Zhang R X, Yang S P 2012 Chin. Phys. B 21 030505
[17] Liu J G 2013 Chin. Phys. B 22 060510
[18] Zhou P, Ding R, Cao Y X 2012 Nonlinear Dyn. 70 1263
[19] Li T, Yu J J, Wang Z 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1796
[20] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强, 刘崇新 2006 55 5055]
[21] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese) [黄丽莲, 齐雪 2013 62 080507]
[22] Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[23] Li G H 2004 Acta Phys. Sin. 53 999 (in Chinese) [李国辉 2004 53 999]
[24] Zhou P, Zhu W 2011 Nonlinear Analysis: Real World Applications 12 811
[25] Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 61 160510]
[26] Chen D Y, Zhang R F, Ma X Y, Wang J 2012 Chin. Phys. B 21 120507
[27] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 (in Chinese) [王发强, 刘崇新 2006 55 3922]
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