Study on Chaotic Dynamics of Perturbed sine-Gordon Equation

ZHANG Wei; WANG Xiu-yan; YAO Ming-hui

doi:10.3969/j.issn.0254-0037.2004.02.002

Journal of Beijing University of Technology > 2004 > 30(2): 134-138. > DOI: 10.3969/j.issn.0254-0037.2004.02.002

ZHANG Wei, WANG Xiu-yan, YAO Ming-hui. Study on Chaotic Dynamics of Perturbed sine-Gordon Equation[J]. Journal of Beijing University of Technology, 2004, 30(2): 134-138. DOI: 10.3969/j.issn.0254-0037.2004.02.002

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Study on Chaotic Dynamics of Perturbed sine-Gordon Equation

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100022, China

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Project supported by Chinese National Foundation of Natural Science(10372008,10328204)

Project supported by Beijing foundation of Natural Science(3032006).

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Received Date: March 18, 2004
Available Online: November 02, 2022

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In order to study the global bifurcations and chaotic dynamics of the truncated sine-Gordon equation with damping and forced exciting, the two-mode truncated sine-Gordon equation is obtained by using the generalized asymptotic inertial manifold. Then, the method of multiple scales is used to find the averaged equations of the two-mode sine-Gordon equation in the case of the primary resonance and 1: 1 internal resonance. With the aid of theory of normal form, the explicit expression of normal form for the averaged equations associated with a pair of double-zero eigenvalues and a pair of pure imaginary eigenvalues is given by using Maple program. Finally, the global perturbation techniques are applied to this normal form to analyze the global bifurcations and chaotic dynamics. The chaotic motion of the two-mode sine-Gordon equation is also found by the numerical simulation.
- sine-Gordon equation,
- normal form,
- global bifurcations,
- chaotic dynamics

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[1]	BISHOP R, FOREST M G, McLAUGHLIN D W, et al. A quasi-periodic route to chaos in a near-integrablePDE[J]. Physica D, 1986, 23: 293-328.
[2]	KOVACIC G, WIGGINS S. Orbits homoclinic to resonance, with an application to chaos in a model of theforced and damped sine-Gordon equation[J]. Physica D, 1992, 57: 185-225.
[3]	TEMAM R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York : Springer-Verlag,1988.
[4]	LIU Z R, XU Z Y, LING G P, et al. Discussion of the dynamical behavior of the sine-Gordon equation[J]. JNonlinear Dynamics in Science and Technology, 1995, 2: 12-30.
[5]	YU P, ZHANG W, BI Q S. Vibration analysis on a thin plate with the aid of computation of normal forms[J].Int J Non-Linear Mech, 2001, 36: 597-627.
[6]	NUSSE H E, YORKE J A. Dynamics: Numerical Explorations[M]. New York: Springer-Verlag, 1997.

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