Parametric instability of linear oscillators with colored time-dependent noise

Separatrix crossing due to multiplicative colored noise

The effect of weak multiplicative colored noise on the dynamics of a Hamiltonian system is studied by means of asymptotic methods, in the vicinity of homoclinic or heteroclinic trajectories. A general expression for the probability of noise-induced separatrix crossing is obtained, and is illustrated by means of a two-well Duffing oscillator. It shows how weak noise can significantly affect the dynamics near separatrices. In addition, the influence of the degree of non-linearity of the noise amplitude is discussed.

经典谐振子单参数Darboux变换得到的奇异参数振子

Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator

该研究通过单参数Darboux变换构造经典谐振子的奇异参数振子，并证明其Ermakov-Lewis不变量与变形参数无关且无奇点。

非线性诱导的对称性破缺：两个参数驱动Kerr-Duffing振荡器系统

Nonlinearity-induced symmetry breaking in a system of two parametrically driven Kerr-Duffing oscillators

本文研究一对非线性耦合的Kerr-Duffing振荡器在参数驱动下的经典动力学，发现即使驱动相同，改变失谐也能使系统从对称解过渡到对称性破缺解。

The nonlinear dynamics of a bistable energy harvesting system with colored noise disturbances

This paper deals with the nonlinear stochastic dynamics of a piezoelectric energy harvesting system subjected to a harmonic external excitation disturbed by Gaussian colored noise. A parametric analysis is conducted, where the effects of the standard deviation and the correlation time of colored noise on the system response are investigated. The numerical results suggest a strong influence of noise on the system response for higher values of correlation time and standard deviation, and a low (noise level independent) influence for low values of correlation time.

Phase-Induced (In)-Stability in Coupled Parametric Oscillators

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $θ$. Being to a large extent analytically solvable, the model reveals a rich $θ$ dependence of the regions of parametric resonance. In particular, the intuitive notion that anti-phase modulations are less prone to parametric resonance is confirmed for sufficiently large coupling and damping. We also compare our results to a recently reported mean field model of collective parametric instability, showing that the two-oscillator model can capture much of the qualitative be…

耦合克尔参量振荡器的参量不稳定性图谱

The parametric instability landscape of coupled Kerr parametric oscillators

本研究针对耦合克尔参量振荡器网络分岔结构不明的问题，采用久期微扰理论绘制其稳定区域图谱，推导了全对等耦合网络分岔转变的解析表达式，明确了类Ising解空间的边界，为实验实现提供指导。