Resonant phase lags of a Duffing oscillator

Stochastic resonance and bifurcation of order parameter in a coupled system of underdamped Duffing oscillators

The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation to ensure that the system can always be relaxed to one of the stationary states as time is long enough. Based on a general framework of the linear response theory, the linear dynamical susceptibility of the system order parameter is explicitly deduced. With the spectral amplification factor as a quantifying index, calculation by the method of moments disclo…

具有衰减扰动与噪声的系统中的非线性共振

Nonlinear resonance in systems with decaying perturbations and noise

本文研究乘性白噪声对时间衰减泵浦非等时系统中共振捕获的影响，结合平均法与随机李雅普诺夫函数给出共振模态随机稳定性条件，并应用于杜芬振子。

具有衰减啁啾频率激励和噪声的非线性系统中的共振

Resonances in nonlinear systems with a decaying chirped-frequency excitation and noise

研究乘性白噪声下强非线性振荡系统在啁啾频率激励中的共振捕获问题，通过平均化方法与随机 Lyapunov 函数分析共振模态的随机稳定性，并应用于 Duffing 振荡器。

Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits

In a recent paper by the author (K. Yagasaki, Nonintegrability of the restricted three-body problem, submitted for publication), a technique was developed for determining whether nearly integrable systems are not meromorphically Bogoyavlenskij-integrable such that the first integrals and commutative vector fields also depend meromorphically on the small parameter. Here we continue to demonstrate the technique for some classes of dynamical systems. In particular, we consider time-periodic perturbations of single-degree-of-freedom Hamiltonian systems and discuss a relationship of the technique w…

具有衰减扰动的耦合非线性振荡器中的共振

Resonance in coupled nonlinear oscillators with decaying perturbations

研究非自治扰动对两个耦合非线性非相同振荡器系统的影响，耦合强度和扰动强度随时间按幂律衰减。通过平均法与李雅普诺夫函数构造导出非自治模型系统，分析锁相状态下共振解稳定性，并用非相同杜芬振荡器系统验证理论结果。