Bifurcations in a Mathieu Equation With Cubic Nonlinearities

By Leslie Ng, Richard H. Rand. Nonlinear Dynamics and Stochastic Mechanics, 2000

73 citations recorded by the source corpus.

We investigate the nonlinear dynamics of the classical Mathieu equation to which is added a nonlinearity which is a general cubic in x, ẋ. 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.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/81398f17d9e946ce4e7fd3d469473012abadc4f0

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In Atomic and Molecular Physics, and Optics

1. Davood Younesian
2. Ramin Sedaghati
3. Ebrahim Esmailzadeh

In Computer Networks and Communications

1. Davood Younesian
2. Ramin Sedaghati
3. Ebrahim Esmailzadeh

In Statistical and Nonlinear Physics

1. Davood Younesian
2. Ramin Sedaghati
3. Ebrahim Esmailzadeh

Citations in the corpus

• Existence of Periodic Solutions for the Generalized Form of Mathieu Equation (2005, methodology): “Ng and Rand used a combination of the averaging and perturbation methods to investigate the classical form of the Mathieu differential equation with cubic form of nonlinearities [ 13 , 14].”