期刊
CHAOS SOLITONS & FRACTALS
卷 14, 期 2, 页码 173-181出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0960-0779(01)00226-0
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We investigate the nonlinear dynamics of the classical Mathieu equation to which is added a nonlinearity which is a general cubic in x, x(over dot). We use a perturbation method (averaging) which is valid in the neighborhood of 2:1 resonance, and in the limit of small forcing and small nonlinearity. By comparing the predictions of first-order averaging with the results of numerical integration, we show that it is necessary to go to second-order averaging in order to obtain the correct qualitative behavior. Analysis of the resulting slow-flow equations is accomplished both analytically as well as by use of the software AUTO. (C) 2002 Elsevier Science Ltd. All rights reserved.
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