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This paper presents a class of quadratic nonlinear system by introducing a linear term x of the third equation into the second equation of a chaotic system based on analyzing and studying some chaos. Using nonlinear dynamics method we analyze the steady, quasi-periodic and chaotic transition process when the system parameter varies. Experiment results are in good agreement with the Matlab simulation results. The Lyapunov exponent of the system with absolute value operation is larger than the original system, and the absolute value operation makes the wing of the original system doubled. Based on Takagi-Sugeno (T-S) fuzzy model and linear matrix inequality, a robust fuzzy controller is designed for the double-wing chaotic system being in asymptotical stability. Simulation results are provided to illustrate the effectiveness of the proposed scheme.
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Keywords:
- double-wing /
- chaos /
- bifurcation /
- linear matrix inequality
[1] Gholizadeh H, Hassannia A, Azarfar A 2013 Chin. Phys. B 22 010503
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[4] [5] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[6] [7] Sun J W, Shen Y, Yin Q, Xu C J 2013 Chaos 23 013140
[8] Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 物理学报 63 010502]
[9] [10] Cang S J, Wang Z H, Chen Z Q, Jia H Y 2014 Nonlinear Dynam. 75 745
[11] [12] [13] Banerjee T, Biswas D 2013 Int. J. Bifurcat. Chaos 23 1330020
[14] Liu W, Wang Z M, Ni M K 2013 Automatica 49 2576
[15] [16] [17] Chen G R, Ueta T 1999 Int. J. Bifurcat. Chaos 9 1465
[18] [19] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[20] [21] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强, 刘崇新 2007 物理学报 56 1983]
[22] [23] Jafari S, Sprott J C, Golpayegani S M R H 2013 Phys. Lett. A 377 699
[24] Molaie M, Jafari S, Sprott J C, Golpayegani S M R H 2013 Int. J. Bifurcat. Chaos 23 1350188
[25] [26] 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 物理学报 58 4469]
[27] [28] Xue W, Qi G Y, Mu J J, Jia H Y, Guo Y L 2013 Chin. Phys. B 22 080504
[29] [30] Luo C, Wang X Y 2014 J. Vib. Control 20 1498
[31] [32] Chen D Y, Liu C F, Wu C, Liu Y J, Ma X Y, You Y J 2012 Circ. Syst. Signal. Pr. 31 1599
[33] [34] [35] Fang Q X 2014 Appl. Math. Comput. 232 381
[36] Ye D, Zhao X G 2014 Nonlinear Dynam. 76 973
[37] [38] [39] Dai L, Sun L, Chen C 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3901
[40] Maeng G, Choi H H 2013 Nonlinear Dynam. 74 571
[41] [42] [43] Wang L 2009 Chaos 19 013107
[44] [45] Giraud L, Haidar A, Saad Y 2010 Numer. Math. Theor. Meth. Appl. 3 276
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[1] Gholizadeh H, Hassannia A, Azarfar A 2013 Chin. Phys. B 22 010503
[2] [3] Xu J X, Guo Z Q, Lee T H 2013 IEEE. T. Ind. Electron. 60 5717
[4] [5] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[6] [7] Sun J W, Shen Y, Yin Q, Xu C J 2013 Chaos 23 013140
[8] Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 物理学报 63 010502]
[9] [10] Cang S J, Wang Z H, Chen Z Q, Jia H Y 2014 Nonlinear Dynam. 75 745
[11] [12] [13] Banerjee T, Biswas D 2013 Int. J. Bifurcat. Chaos 23 1330020
[14] Liu W, Wang Z M, Ni M K 2013 Automatica 49 2576
[15] [16] [17] Chen G R, Ueta T 1999 Int. J. Bifurcat. Chaos 9 1465
[18] [19] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[20] [21] Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强, 刘崇新 2007 物理学报 56 1983]
[22] [23] Jafari S, Sprott J C, Golpayegani S M R H 2013 Phys. Lett. A 377 699
[24] Molaie M, Jafari S, Sprott J C, Golpayegani S M R H 2013 Int. J. Bifurcat. Chaos 23 1350188
[25] [26] 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 物理学报 58 4469]
[27] [28] Xue W, Qi G Y, Mu J J, Jia H Y, Guo Y L 2013 Chin. Phys. B 22 080504
[29] [30] Luo C, Wang X Y 2014 J. Vib. Control 20 1498
[31] [32] Chen D Y, Liu C F, Wu C, Liu Y J, Ma X Y, You Y J 2012 Circ. Syst. Signal. Pr. 31 1599
[33] [34] [35] Fang Q X 2014 Appl. Math. Comput. 232 381
[36] Ye D, Zhao X G 2014 Nonlinear Dynam. 76 973
[37] [38] [39] Dai L, Sun L, Chen C 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3901
[40] Maeng G, Choi H H 2013 Nonlinear Dynam. 74 571
[41] [42] [43] Wang L 2009 Chaos 19 013107
[44] [45] Giraud L, Haidar A, Saad Y 2010 Numer. Math. Theor. Meth. Appl. 3 276
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