Parametric autoresonance

Abstract

We investigate parametric autoresonance: a persisting phase locking which occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and unarrested by the oscillator nonlinearity. The system has three characteristic time scales, the fastest one corresponding to the natural frequency of the oscillator. We perform averaging over the fastest time scale and analyze the reduced set of equations analytically and numerically. Analytical results are obtained by exploiting the scale separation between the two remaining time scales which enables one to use the adiabatic invariant of the perturbed nonlinear motion.

8 pages, 10 figures

References in corpus (1)

• Amplitude measurements of Faraday waves

Cited by in corpus (10)

• Parametric Autoresonance in Faraday waves
• Experimental Study of Parametric Autoresonance in Faraday Waves
• Quantum phenomena in a chirped parametric anharmonic oscillator
• Autoresonance in oscillating systems with combined excitation and weak dissipation
• Bifurcations of autoresonant modes in oscillating systems with combined excitation
• Capture into parametric autoresonance in the presence of noise
• Autoresonance in a Dissipative System
• Constraining the mass and moment of inertia of neutron stars from quasi-periodic oscillations in X-ray binaries
• Asymptotic analysis of the autoresonance capture in oscillating systems with combined excitation
• Stability of parametric autoresonance under random perturbations