Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(3): 030509    DOI: 10.1088/1674-1056/19/3/030509
GENERAL Prev   Next  

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

Wang Hao-Xiang(汪浩祥), Cai Guo-Liang(蔡国梁), Miao Sheng(缪盛), and Tian Li-Xin(田立新)
Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China
Abstract  This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.
Keywords:  hyperchaos      nonlinear feedback control      Lyapunov exponents      chaos circuit  
Received:  07 August 2009      Revised:  24 August 2009      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  02.30.Oz (Bifurcation theory)  
  84.30.Bv (Circuit theory)  
  02.30.Yy (Control theory)  
Fund: Project supported by the National Natural Science Foundations of China (Grant Nos.~70571030 and 90610031), the Society Science Foundation from Ministry of Education of China (Grant No.~08JA790057) and the Advanced Talents' Foundation and Student's Foundation of Jiangsu University (Grant Nos.~07JDG054 and 07A075).

Cite this article: 

Wang Hao-Xiang(汪浩祥), Cai Guo-Liang(蔡国梁), Miao Sheng(缪盛), and Tian Li-Xin(田立新) Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 2010 Chin. Phys. B 19 030509

[1] Cai G L, Zheng S and Tian L X 2008 Chin. Phys. B 17 2412
[2] Cai G L and Huang J J 2007 J. Jiangsu Uni . 28 269
[3] Jia H Y, Chen Z Q and Yuan Z Z 2009 Acta Phys. Sin. 58 4469 (in Chinese)
[4] Luo X H 2009 Chin. Phys. B 18 3304
[5] Cai G L and Huang J J 2007 Int. J. Nonli. Sci. 3 213
[6] Zhou P, Wei L J and Chen X F 2009 Chin. Phys. B 18 2674
[7] Luo X H, Zhou W, Li R, Liang Y L and Luo M W 2009 Chin. Phys. B 18 2168
[8] Lü J, Chen T and Zhang S 2002 Chaos, Solitons and Fractals 14 529
[9] Cai G L and Huan J J 2006 Acta Phys. Sin. 55 3997 (in Chinese)
[10] R?ssler O E 1979 Phys. Lett. A 71 155
[11] Kapitaniak T and Chua L O 1994 Int. J. Bifur. Chaos 4 477
[12] Chen A, Lu J, Lü J and Yu S M 2006 Phys. A 364 103
[13] Wang F and Liu C 2006 Chin. Phys. 15 0963
[14] Jia Q 2007 Phys. Lett. A 3 217
[15] Wang G, Zhang X, Zheng Y and Li Y 2006 Phys. A 371 260
[16] Cai G L, Zheng S and Tian L X 2008 Chin. Phys. B 17 4039
[17] Gao T, Chen Z, Gu Q and Yuan Z 2008 Chaos, Solitons and Fractals 35 390
[18] Cai G L, Zheng S and Tan Z M 2008 J. Inf. and Comp. Sci . 3 49
[19] Wolf, Swift J, Swinney H and Vastano J 1985 Phys. D 16 285
[1] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[2] A memristive map with coexisting chaos and hyperchaos
Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). Chin. Phys. B, 2021, 30(11): 110502.
[3] Control of fractional chaotic and hyperchaotic systems based on a fractional order controller
Li Tian-Zeng (李天增), Wang Yu (王瑜), Luo Mao-Kang (罗懋康). Chin. Phys. B, 2014, 23(8): 080501.
[4] The dynamics of a symmetric coupling of three modified quadratic maps
Paulo C. Rech. Chin. Phys. B, 2013, 22(8): 080202.
[5] The synchronization of a fractional order hyperchaotic system based on passive control
Wu Chao-Jun(吴朝俊), Zhang Yan-Bin(张彦斌), and Yang Ning-Ning(杨宁宁). Chin. Phys. B, 2011, 20(6): 060505.
[6] Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions
Ri Ilmyong(李日明), Feng Yu-Ling(冯玉玲), Yao Zhi-Hai(姚治海), and Fan Jian(范健) . Chin. Phys. B, 2011, 20(12): 120504.
[7] A novel chaotic system with one source and two saddle-foci in Hopfield neural networks
Chen Peng-Fei(陈鹏飞), Chen Zeng-Qiang(陈增强), and Wu Wen-Juan(吴文娟). Chin. Phys. B, 2010, 19(4): 040509.
[8] Study on eigenvalue space of hyperchaotic canonical four-dimensional Chua's circuit
Li Guan-Lin(李冠林) and Chen Xi-You(陈希有). Chin. Phys. B, 2010, 19(3): 030507.
[9] A novel one equilibrium hyper-chaotic system generated upon Lü attractor
Jia Hong-Yan(贾红艳), Chen Zeng-Qiang(陈增强), and Yuan Zhu-Zhi(袁著祉). Chin. Phys. B, 2010, 19(2): 020507.
[10] Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems
Jia Li-Xin(贾立新), Dai Hao(戴浩), and Hui Meng(惠萌). Chin. Phys. B, 2010, 19(11): 110509.
[11] A hyperchaotic system stabilization via inverse optimal control and experimental research
Yang Ning-Ning(杨宁宁), Liu Chong-Xin(刘崇新), and Wu Chao-Jun(吴朝俊). Chin. Phys. B, 2010, 19(10): 100502.
[12] Circuitry implementation of a novel nonautonomous hyperchaotic Liu system based on sine input
Luo Xiao-Hua(罗小华). Chin. Phys. B, 2009, 18(8): 3304-3308.
[13] A novel four-dimensional autonomous hyperchaotic system
Liu Chong-Xin(刘崇新) and Liu Ling(刘凌). Chin. Phys. B, 2009, 18(6): 2188-2193.
[14] Fuzzy modeling and impulsive control of hyperchaotic Lü system
Zhang Xiao-Hong(张小洪) and Li Dong(李东). Chin. Phys. B, 2009, 18(5): 1774-1779.
[15] Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system
Gu Qiao-Lun(顾巧论) and Gao Tie-Gang(高铁杠). Chin. Phys. B, 2009, 18(1): 84-90.
No Suggested Reading articles found!