Parameter estimation for chaotic systems with and without noise using differential evolution-based method

doi:10.1088/1674-1056/20/6/060502

Abstract We present an approach in which the differential evolution (DE) algorithm is used to address identification problems in chaotic systems with or without delay terms. Unlike existing considerations, the scheme is able to simultaneously extract (i) the commonly considered parameters, (ii) the delay, and (iii) the initial state. The main goal is to present and verify the robustness against the common white Guassian noise of the DE-based method. Results of the time-delay logistic system, the Mackey-Glass system and the Lorenz system are also presented.

Keywords: chaotic system differential evolution noise parameter estimation

Received: 04 December 2010
Revised: 24 January 2011
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	74.70.De

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60976039).

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Li Nian-Qiang (李念强), Pan Wei (潘炜), Yan Lian-Shan (闫连山), Luo Bin (罗斌), Xu Ming-Feng (徐明峰), Jiang Ning (江宁) Parameter estimation for chaotic systems with and without noise using differential evolution-based method 2011 Chin. Phys. B 20 060502

[1]	Li X F, Pan W, Luo B and Ma D 2006 IEEE J. Quantum Electron. 42 953
[2]	Zhang W L, Pan W, Luo B, Zou X H, Wang M Y and Zhou Z 2008 Opt. Lett. 33 237
[3]	Rontani D, Locquet A, Sciamanna M, Citrin D S and Ortin S 2009 IEEE J. Quantum Electron. 45 879
[4]	Wu J G, Xia G Q and Wu Z M 2009 Opt. Express 17 20124
[5]	Parlitz U and Junge L 1996 Phys. Rev. E 54 6253
[6]	Parlitz U 1996 Phys. Rev. Lett. 76 1232
[7]	Rakshit B, Chowdury A R and Saha P 2007 Chaos, Solitons & Fractals 32 1278
[8]	Abarbanel H D I, Creveling D R and Jeanne J M 2008 Phys. Rev. E 77 016208
[9]	Quinn J C, Bryant P H, Creveling D R, Klein S R and Abarbanel D I 2009 Phys. Rev. E 80 016201
[10]	Alvarez G, Montoya F, Romera M and Pastor G 2003 Phys. Lett. A 311 172
[11]	Wu X G, Hu H P and Zhang B L 2004 Chaos, Solitons & Fractals 22 359
[12]	Chen Z, Zeng Y C and Fu Z J 2008 Acta Phys. Sin. 57 46 (in Chinese)
[13]	Piccardi C 2006 Chaos 16 043115
[14]	Dai D, Ma X K, Li F C and You Y 2002 Chin. Phys. 11 2459
[15]	He Q, Wang L and Liu B 2007 Chaos, Solitons & Fractals 34 654
[16]	Gao F, Liu Z Q and Tong H Q 2008 Chin. Phys. B 17 1196
[17]	Li L X, Yang Y, Peng H P and Wang X D 2006 Chaos, Solitons & Fractals 28 1204
[18]	Chang W D 2007 Chaos, Solitons & Fractals 29 1047
[19]	Peng B, Liu B, Zhang F Y and Wang L 2009 Chaos, Solitons & Fractals 39 2110
[20]	Tang Y G and Guan X P 2009 Chaos, Solitons & Fractals 42 3132
[21]	Price K and Storn R, Differential evolution homepage. Available from: http://www.ICSI.Berkeley.edu/ sim storn/code.html
[22]	Pyragas K 1998 Phys. Rev. E 58 3067
[23]	Ponomarenko V I and Prokhorov M D 2002 Phys. Rev. E 66 026215
[24]	Shahverdiev E M, Nuriev R A, Hashimov R H and Shore K A 2006 Chaos, Solitons & Fractals 29 854
[25]	Lorenz E N 1963 J. Atmos. Sci. 20 130

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Parameter estimation for chaotic systems with and without noise using differential evolution-based method

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