This paper describes how parametric resonances associated with a galactic potential subjected to relatively low amplitude, strictly periodic time-dependent perturbations can be impacted by pseudo-random variations in the pulsation frequency, modeled as coloured noise. One aim thereby is to allow for the effects of a changing oscillation frequency as the density distribution associated with a ga...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

In this work, parametric noise squeezing and parametric resonance are realized through the use of an electronic feedback circuit to excite a microcantilever with a signal proportional to the product of the microcantilever's displacement and a harmonic signal. The cantilever's displacement is monitored using an optical lever technique. By adjusting the gain of an amplifier in the feedback circui...

Parametric resonance is a type of nonlinear vibration phenomenon [1], [2] induced from the periodic modulation of at least one of the system parameters and has the potential to exhibit interesting higher order nonlinear behaviour [3]. Parametrically excited vibration energy harvesters have been previously shown to enhance both the power amplitude [4] and the frequency bandwidth [5] when compare...

A theoretical study of parametric processes near the electron cyclotron resonance region in tokamak plasmas is presented. Parametric dispersion relations, including finite wave length of the driver pump, of principal and harmonic parametric excitations, are given. The problem of primary and secondary decays including their temporal and spatial growth rates is studied. In the nonlinear phase of ...

We propose a nonparametric procedure to test the hypothesis that the j-th largest eigenvalues of a covariance matrix are equal in multipopulation. We apply the Mood test by using the principal component scores and deal the equality of eigenvalues with the equality of variance. We investigate the significance level and the power of test by simulation and show that this nonparametric test is usef...

Functional principal component analysis (FPCA) is a popular approach in functional data analysis to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). Most existing FPCA approaches use a set of flexible basis functions such as B-spline basis to represent the FPCs, and control the smoothness...

The stochastic model of cool-flame combustion a hydrocarbon mixture is considered. For this 3D model, noise excitement large-amplitude oscillations in the parametric zone, where deterministic has single equilibrium attractor, studied. By statistics interspike intervals, phenomenon anti-coherence resonance revealed. To estimate threshold intensities that causes excitement, sensitivity technique ...