Estimating the bound for the generalized Lorenz system

doi:10.1088/1674-1056/19/1/010505

Abstract A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.

Keywords: chaos generalized Lorenz system Lyapunov function Lagrange multiplier method

Received: 10 October 2008
Revised: 15 July 2009
Published: 15 January 2010

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	05.45.Gg	(Control of chaos, applications of chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60674059), and Research Fund of University of Science and Technology Beijing, China (Grant No. 00009010).

Cite this article:

Zheng Yu, Zhang Xiao-Dan Estimating the bound for the generalized Lorenz system 2010 Chin. Phys. B 19 010505

[1]	Lorenz E N 1963 J. Atoms. Sci. 20 130
[2]	Chen G R and Ueta T 1999 Int. J. Bifurc. Chaos 9 1465
[3]	Lü J H and Chen G R 2002 Int. J. Bifurc. Chaos 12 659
[4]	Van\v e\v cek A and \v Celikovsk\v y S 1996 Control Systems: from Linear Analysis to Synthesis of Chaos (London: Prentice-Hall)
[5]	Chen G R and Lü J H 2001 The Lorenz Family System Dynamics Analysis, Control and Synchronization (Beijing: Science Press) p151
[6]	Cai N, Jing Y W and Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)
[7]	Zhang X D and Zhang L L 2006 Commun. Theor. Phys. 45 461
[8]	Niu Y D, Ma W Q and Wang Y 2009 Acta Phys. Sin. 58 2934 (in Chinese)
[9]	Zhang X D, Zhang L L and Min L Q 2003 Chin. Phys. Lett. 20 2114
[10]	W D Q and Luo X S 2008 Chin. Phys. B 17 92
[11]	Yan S L 2007 Chin. Phys. 16 3271
[12]	Wang S, Cai L, Li Q and Wu G 2007 Chin. Phys. 16 2631
[13]	Leonov G, Bunin A and Koksch N 1987 ZAMM 67 649
[14]	Zhou T, Tang Y and Chen G R 2003 Int. J. Bifurc. Chaos 13 2561
[15]	Li D M, Lu J A, Wu X Q and Chen G R 2005 Chaos, Solitons and Fractals 23 529
[16]	Li D M, Lu J A, Wu X Q and Chen G R 2006 J. Math. Appl. 323 844

[1]	Quantum to classical transition induced by a classically small influence Wen-Lei Zhao(赵文垒), Quanlin Jie(揭泉林). Chin. Phys. B, 2020, 29(8): 080302.
[2]	Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Chin. Phys. B, 2020, 29(5): 050504.
[3]	Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator Hong-Bo Yan(闫洪波), Hong Gao(高鸿), Gao-Wei Yang(杨高炜), Hong-Bo Hao(郝宏波), Yu Niu(牛禹), Pei Liu(刘霈). Chin. Phys. B, 2020, 29(2): 020504.
[4]	Chaotic dynamics of complex trajectory and its quantum signature Wen-Lei Zhao(赵文垒), Pengkai Gong(巩膨恺), Jiaozi Wang(王骄子), and Qian Wang(王骞). Chin. Phys. B, 2020, 29(12): 120302.
[5]	Nonlinear dynamics in non-volatile locally-active memristor for periodic and chaotic oscillations Wen-Yu Gu(谷文玉), Guang-Yi Wang(王光义), Yu-Jiao Dong(董玉姣), Jia-Jie Ying(应佳捷). Chin. Phys. B, 2020, 29(11): 110503.
[6]	Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system Fei Gao(高飞), Wen-Qin Li(李文琴), Heng-Qing Tong(童恒庆), Xi-Ling Li(李喜玲). Chin. Phys. B, 2019, 28(9): 090501.
[7]	Dynamical stable-jump-stable-jump picture in a non-periodically driven quantum relativistic kicked rotor system Hsincheng Yu(于心澄), Zhongzhou Ren(任中洲), Xin Zhang(张欣). Chin. Phys. B, 2019, 28(2): 020504.
[8]	Design new chaotic maps based on dimension expansion Abdulaziz O A Alamodi, Kehui Sun(孙克辉), Wei Ai(艾维), Chen Chen(陈晨), Dong Peng(彭冬). Chin. Phys. B, 2019, 28(2): 020503.
[9]	Enhancing von Neumann entropy by chaos in spin-orbit entanglement Chen-Rong Liu(刘郴荣), Pei Yu(喻佩), Xian-Zhang Chen(陈宪章), Hong-Ya Xu(徐洪亚), Liang Huang(黄亮), Ying-Cheng Lai(来颖诚). Chin. Phys. B, 2019, 28(10): 100501.
[10]	Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards Runzu Zhang(张润祖), Weihua Zhang(张为华), Barbara Dietz, Guozhi Chai(柴国志), Liang Huang(黄亮). Chin. Phys. B, 2019, 28(10): 100502.
[11]	Dynamic characteristics in an external-cavity multi-quantum-well laser Sen-Lin Yan(颜森林). Chin. Phys. B, 2018, 27(6): 060501.
[12]	A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control Jay Prakash Singh, Binoy Krishna Roy, Zhouchao Wei(魏周超). Chin. Phys. B, 2018, 27(4): 040503.
[13]	Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays Li-Yuan Ma(马立媛), Jia-Liang Ji(季佳梁), Zong-Wei Xu(徐宗玮), Zuo-Nong Zhu(朱佐农). Chin. Phys. B, 2018, 27(3): 030201.
[14]	Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem Zeyu Liu(刘泽宇), Tiecheng Xia(夏铁成), Jinbo Wang(王金波). Chin. Phys. B, 2018, 27(3): 030502.
[15]	Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems Wenjing Xu(徐文静), Wei Xu(徐伟), Li Cai(蔡力). Chin. Phys. B, 2018, 27(11): 110201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed

Metrics
Related Articles