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Asymptotic analysis of strongly nonlinear oscillators. (English) Zbl 0585.34039

In the paper the asymptotic method is applied for the analysis of a strongly nonlinear autonomous oscillator characterised by the differential equation \(\ddot u+g(u)=\epsilon f(u,\dot u)\) with a small parameter \(\epsilon >0\). The equations for the amplitude and phase factor are obtained and the amplitude and stability of the corresponding limit cycles are determined.
Reviewer: J.Mika

MSC:

34E15 Singular perturbations for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C29 Averaging method for ordinary differential equations
34D15 Singular perturbations of ordinary differential equations
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References:

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