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Keywords: Duffing equation
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Journal Articles

On the Formal Equivalence of Normal Form Theory and the Method of Multiple Time Scales

Fengxia Wang, Anil K. Bajaj
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2009, 4(2): 021005.
https://doi.org/10.1115/1.3079824
Published Online: March 6, 2009
... solution at each step of approximation in the process of obtaining modulation equations. Note that in Eq. 70 we have set the contributions from null space of the linear operator L equal to zero, as was done for the Duffing equation example. Next, substituting the O ( ε 2...
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Topics: Differential equations, Resonance, Nonlinear systems, Dynamic systems, Degrees of freedom, Pendulums, Nonlinear dynamical systems, Eigenvalues, Springs, Dynamics (Mechanics)
Journal Articles

A Coupled Motion of the Thermally Induced Fluid Convection and the Membrane Motion

Xiaoling He
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. July 2008, 3(3): 031005.
https://doi.org/10.1115/1.2908258
Published Online: April 30, 2008
... response in Z . From 24a , 24b , it is apparent that the response of Y is independent of Z . Therefore, Y is continuous. The Duffing equation is normalized to the same time scale as that of the Lorenz oscillator in order to synchronize the two oscillators, i.e., W , τ...
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Topics: Attractors, Bifurcation, Chaos, Convection, Flow (Dynamics), Fluids, Membranes, Oscillations, Stability, Transients (Dynamics)