High frequency forcing on nonlinear systems

doi:10.1088/1674-1056/22/3/030503

Abstract High-frequency signals are pervasive in many science and engineering fields. In this work, the effect of high-frequency driving on general nonlinear systems is investigated, and an effective equation for the slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions. Based on this theory, a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency. Numerical simulations on several nonlinear oscillator systems show very good agreements with the theoretic result. These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.

Keywords: high frequency nonlinear oscillator inertial approximation phase transitions

Received: 06 July 2012
Revised: 24 August 2012
Accepted manuscript online:

PACS:	05.40.Ca	(Noise)
	87.16.dj	(Dynamics and fluctuations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11205103 and 11075202).

Corresponding Authors: Zhan Meng
E-mail: zhanmeng@wipm.ac.cn

Cite this article:

Yao Cheng-Gui (姚成贵), He Zhi-Wei (何志威), Zhan Meng (占萌) High frequency forcing on nonlinear systems 2013 Chin. Phys. B 22 030503

[1]	Strogatz S H 1994 Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Massachusetts: Perseus Books Publishing)
[2]	Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press)
[3]	Perez R and Glass L 1982 Phys. Lett. A 90 441
[4]	Ding E J 1986 Phys. Rev. A 34 3547
[5]	Parlitz U and Lauterborn W 1987 Phys. Rev. A 36 1428
[6]	Rajasekar S and Lakshmanan M 1988 Physica D 32 146
[7]	Linsay P S 1981 Phys. Rev. Lett. 47 1349
[8]	Kao Y H and Wang C S 1993 Phys. Rev. E 48 2514
[9]	Pivka L, Zheleznyak A L and Chua L O 1994 Inter. J. Bifur. Chaos Appl. Sci. Eng. 4 1743
[10]	Glass L, Guevara M R and Perez A S R 1983 Physica D 7 89
[11]	Epstein I R and Pojman J A 1998 An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos, Topics in Physical Chemistry (New York: Oxford University Press)
[12]	Tai C F, Groat W C and Roppolo J R 2005 IEEE Trans. Neural. Syst. Rehabil. Eng. 13 415
[13]	Tai C F, Groat W C and Roppolo J R 2005 IEEE Trans. Neural. Syst. Rehabil. Eng. 52 1323
[14]	Bhadra N, Lahowetz E A, Foldes S T and Kilgore K L 2007 J. Comput. Neurosci. 22 313
[15]	Wang L Y and Kaczmarek L K 1998 Nature 394 384
[16]	Koblischka M R, Wei J D, Kirsch M and Hartmann U 2006 Jpn. J. Appl. Phys. 45 2238
[17]	Blekhman I I 2000 Vibrational Mechanics. Nonlinear Dynamic Effects, General Approach, Applications (Singapore: World Scientific Press)
[18]	Blekhman I I 2004 Selected Topics in Vibrational Mechanics (Singapore: World Scientific Press)
[19]	Thomsen J J 2005 Inter. J. Bifur. Chaos 15 2799
[20]	Thomsen J J 2008 J. Sound Vibr. 311 1249
[21]	Kivshar Y S, Rodelsperger P and Benner H 1994 Phys. Rev. E 49 319
[22]	Landa P S and McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433
[23]	Liang R Y, Xi J, Zhao L, Zou C R and Wei C H 2012 Acta. Phys. Sin. 61 134305 (in Chinese)
[24]	Zhang L, Zhong S C and Peng H 2012 Acta. Phys. Sin. 61 130503 (in Chinese)
[25]	Wang C J 2012 Acta. Phys. Sin. 61 010503 (in Chinese)
[26]	Jiang L L, Luo X Q and Wu D 2012 Chin. Phys. B 21 090503
[27]	Yang J H and Liu X B 2010 Chin. Phys. B 19 050504
[28]	Ullner E, Zaikin A, García-Ojalvo J, Bascones R and Kurths J 2003 Phys. Lett. A 312 348
[29]	Deng B, Wang J, Wei X L, Tsang K M and Chan W L 2010 Chaos 20 013113
[30]	Deng B, Wang J and Wei X L 2009 Chaos 19 013117
[31]	Cubero D, Baltanás J P and Casado-Pascual J 2006 Phys. Rev. E 73 061102
[32]	Blekhman I I and Landa P S 2004 Int. J. Non-Linear Mech. 39 421
[33]	Casado-Pascual J and Baltanás J P 2004 Phys. Rev. E 69 046108
[34]	Chizhevsky V N and Giacomelli G 2006 Phys. Rev. E 73 022103
[35]	Chizhevsky V N and Giacomelli G 2004 Phys. Rev. E 70 062101
[36]	Chizhevsky V N and Giacomelli G 2005 Phys. Rev. A 71 011801
[37]	Khovanov I A and McClintock P V E 2007 Phys. Rev. E 76 031122
[38]	Yao C G and Zhan M 2010 Phys. Rev. E 81 061129
[39]	Yao C G, Liu Y and Zhan M 2011 Phys. Rev. E 83 061122
[40]	Gandhimathi V M, Rajasekar S and Kurths J 2006 Phys. Lett. A 360 279
[41]	Jeyakumari S, Chinnathambi V, Rajasekar S and Sanjuan M A F 2009 Phys. Rev. E 80 046608
[42]	Jeyakumari S, Chinnathambi V, Rajasekar S and Sanjuan M A F 2009 Chaos 19 043128
[43]	Zaikin A A, López L, Baltanás J P, Kurths J and Sanjuan M A F 2002 Phys. Rev. E 66 011106
[44]	Gandhimathi V M, Rajasekar S and Kurths J 2006 Phys. Lett. A 360 279
[45]	Chizhevsky V N, Smeu E and Giacomelli G 2003 Phys. Rev. Lett. 91 220602
[46]	Baltanás J P, López L, Blechman I I, Landa P S, Zaikin A, Kurths J and Sanjuan M A F 2003 Phys. Rev. E 67 066119
[47]	Hu G, Ditzinger T, Ning C Z and Haken H 1993 Phys. Rev. Lett. 71 807
[48]	Rappel W J and Strogatz S H 1994 Phys. Rev. E 50 3249
[49]	Meucci R, Gadomski W, Ciofini M and Arecchi F T 1994 Phys. Rev. E 49 R2528
[50]	Qu Z L, Hu G, Yang G and Qin G R 1995 Phys. Rev. Lett. 74 1736

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