耦合耗散动力系统的例外点
Exceptional points in coupled dissipative dynamical systems
摘要：
基于定态附近的线性分析，我们研究了耦合耗散动力系统的瞬态行为。我们发现在一组特定的系统参数下，过渡时间最小，并且在此参数下，雅可比矩阵的两个特征值和两个特征向量同时合并，这个退化点称为例外点。对于耦合极限环振子的情形，我们研究了振幅死态的瞬态行为，阐明了异常点与频率锁定的临界点以及包络振荡的转变有关。
英文摘要：
We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of Jacobian matrix coalesce at the same time, this degenerate point is called the exceptional point. For the case of coupled limit cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.
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