Asymptotic stability of forced oscillations emanating from a limit cycle

Globally and locally attractive solutions for quasi-periodically forced systems

We consider a class of differential equations, $\ddot x + γ\dot x + g(x) = f(ωt)$, with $ω\in {\bf R}^{d}$, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of the limit cycle described by the trajectory with the same quasi-periodicity as the forcing. For $g(x)=x^{2p+1}$, $p\in {\bf N}$, we show that, when the dissipation coefficient is large enough, there is only one limit cycle and that it is a global attractor. In the case of other forces, including $g(x)=x^{2p}$ (with $p=1$ describing the varacto…

周期受迫三区域方程中的七个极限环

Seven Limit Cycles in a Periodically Forced Three-Zone Equation

本文针对带连续三区域分段线性非线性项的周期受迫标量方程，构造七环示例，通过符号积分等方法得到特定有理参数，结合泰勒估计等在相柱上确定至少七个孤立周期轨道。

对角受迫系统与矩阵环的谱特征

Diagonally forced systems and the spectral signature of matrix cycles

本文研究对角元素为负的矩阵经变量 $σ$ 缩放后的稳定性临界值，建立特征多项式根与缩放特征值的等价关系，并据此分离主导反馈环、提出矩阵的内在谱特征。