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在对已有的混沌系统分析和研究的基础上,将一个二次混沌系统第三个方程关于x的线性项引入到第二个方程中,通过对该系统第二个等式中的线性项x作绝对值运算,提出了一类新的二次非线性系统. 采用非线性动力学方法分析了系统参数变化时所经历的稳定、准周期、混沌的过渡过程,模拟电路实验结果与Matlab数值仿真结果相一致. 分析发现混沌态时绝对值运算后的系统比原系统的Lyapunov指数更大,并可将原系统的混沌吸引子由两个翼的拓扑结构变为四翼的拓扑结构,从而实现羽翼倍增. 针对该混沌特性更强的羽翼倍增混沌系统,基于Takagi-Sugeno(T-S)模糊模型和线性矩阵不等式(LMI),设计出使该羽翼倍增混沌系统渐近稳定的鲁棒模糊控制器. 仿真结果证实了所提出定理和设计控制器的有效性.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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[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]
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[14] Liu W, Wang Z M, Ni M K 2013 Automatica 49 2576
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[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]
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[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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