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

doi:10.1088/1674-1056/19/3/030509

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30509-030509.doi: 10.1088/1674-1056/19/3/030509

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

汪浩祥, 蔡国梁, 缪盛, 田立新

Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China

收稿日期:2009-08-07 修回日期:2009-08-24 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
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).

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

Received:2009-08-07 Revised:2009-08-24 Online:2010-03-15 Published:2010-03-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: hyperchaos, nonlinear feedback control, Lyapunov exponents, chaos circuit

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

05.45.Pq (Numerical simulations of chaotic systems) 02.30.Oz (Bifurcation theory) 84.30.Bv (Circuit theory) 02.30.Yy (Control theory)

汪浩祥, 蔡国梁, 缪盛, 田立新. Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation[J]. 中国物理B, 2010, 19(3): 30509-030509.

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[J]. Chin. Phys. B, 2010, 19(3): 30509-030509.

参考文献 19

[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

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

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 19

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). A color image encryption algorithm based on hyperchaotic map and DNA mutation[J]. 中国物理B, 2023, 32(3): 30501-030501.
[2]	Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map[J]. 中国物理B, 2023, 32(3): 30504-030504.
[3]	Xing-Yuan Wang(王兴元), Xiao-Li Wang(王哓丽), Lin Teng(滕琳), Dong-Hua Jiang(蒋东华), and Yongjin Xian(咸永锦). Lossless embedding: A visually meaningful image encryption algorithm based on hyperchaos and compressive sensing[J]. 中国物理B, 2023, 32(2): 20503-020503.
[4]	Chunlei Fan(范春雷) and Qun Ding(丁群). A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain[J]. 中国物理B, 2023, 32(1): 10501-010501.
[5]	Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application[J]. 中国物理B, 2022, 31(11): 110501-110501.
[6]	Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree[J]. 中国物理B, 2022, 31(11): 110503-110503.
[7]	Peng-Fei Fang(方鹏飞), Han Liu(刘涵), Cheng-Mao Wu(吴成茂), and Min Liu(刘旻). Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model[J]. 中国物理B, 2022, 31(4): 40501-040501.
[8]	Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network[J]. 中国物理B, 2022, 31(2): 20502-020502.
[9]	Chenguang Ma(马晨光), Santo Banerjee, Li Xiong(熊丽), Tianming Liu(刘天明), Xintong Han(韩昕彤), and Jun Mou(牟俊). Dynamical analysis, circuit realization, and application in pseudorandom number generators of a fractional-order laser chaotic system[J]. 中国物理B, 2021, 30(12): 120504-120504.
[10]	Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷). Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation[J]. 中国物理B, 2021, 30(12): 120502-120502.
[11]	Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay[J]. 中国物理B, 2021, 30(12): 120503-120503.
[12]	Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan. Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control[J]. 中国物理B, 2021, 30(12): 120512-120512.
[13]	Sixiao Kong(孔思晓), Chunbiao Li(李春彪), Shaobo He(贺少波), Serdar Çiçek, and Qiang Lai(赖强). A memristive map with coexisting chaos and hyperchaos[J]. 中国物理B, 2021, 30(11): 110502-110502.
[14]	Hai-Fang Liu(刘海芳), Yun-Cai Wang(王云才), Lu-Xiao Sang(桑鲁骁), and Jian-Guo Zhang(张建国). Physical generation of random numbers using an asymmetrical Boolean network[J]. 中国物理B, 2021, 30(11): 110503-110503.
[15]	Qi Li(李琦), Xingyuan Wang(王兴元), He Wang(王赫), Xiaolin Ye(叶晓林), Shuang Zhou(周双), Suo Gao(高锁), and Yunqing Shi(施云庆). A secure image protection algorithm by steganography and encryption using the 2D-TSCC[J]. 中国物理B, 2021, 30(11): 110501-110501.