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Insight into the dynamic behaviour of the Van der Pol/Raleigh oscillator using the internal stiffness and damping forces
(2016-10-03)
The van der Pol oscillator is an archetypal nonlinear oscillator that has been studied for many years. It is a self-sustaining oscillator that vibrates in a limit cycle, and has the characteristic that it generates energy ...
Frequency domain unsteady transonic aerodynamics for flutter and limit cycle oscillation prediction
(Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM, 2010)
The purpose of this study was to develop new approaches for predicting transonic flutter and limit cycle oscillations (LCO) using computational methods. The TSD equation is separated into the in-phase and out-of-phase ...
Leaking elastic capacitor as model for active matter
(2021-05-24)
We introduce the “leaking elastic capacitor” (LEC) model, a nonconservative dynamical system that combines simple electrical and mechanical degrees of freedom. We show that an LEC connected to an external voltage source ...
On limit cycle approximations in the van der Pol oscillator
(Elsevier Science, 2005-01)
This paper applies bifurcation analysis to the well-known van der Pol oscillator to obtain approximations of its periodic solutions in the nearly sinusoidal regime. A frequency domain method based on harmonic balance ...
Controlling oscillation amplitudes via feedback
(World Scientific, 2000-12)
This paper studies feedback control of limit cycle amplitudes in nonlinear systems. A graphical approach to bifurcation control is first briefly introduced, followed by the derivation of a nonlinear control law. Then, a ...
High order analysis of the limit cycle of the van der Pol oscillator
(American Institute of Physics, 2018-01)
We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé ...
Relaxation oscillation in planar discontinuous piecewise smooth fast–slow systems
(2022-01-01)
This paper provides a geometric analysis of relaxation oscillations in the context of planar fast–slow systems with a discontinuous right-hand side. We give conditions that guarantee the existence of a stable crossing limit ...
Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
(World Scientific, 2007-12)
A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the ...
Forced duffing oscillator
(Wolfram Demonstration Project, 2016)
Forced duffing oscillator
(Wolfram Demonstration Project, 2011)