周期性切换耦合振荡器系统中的相移反转
Phase-shift inversion in oscillator systems with periodically switching couplings
摘要：
系统对外部周期性变化的响应可以提供有关其动力学性质的关键信息。我们调查的同步过渡，一个典型的例子，一个动态的相变，在这样一个时间响应的框架。在周期性开关作用下的仓本模型具有与原始平均场模型相同的相变类型。此外，我们看到同步跃迁的特征也出现在序参量相对于振荡相互作用相位的相对延迟中。具体地说，相移变得显着更大的系统变得更接近相变，使得在最小的相互作用密度的序参量甚至可以大于在最大的相互作用密度，违反直觉。我们认为，这种相移反转是由发散的弛豫时间，以类似的方式在动力学伊辛模型的临界点附近的共振。我们的结果，基于对全局耦合系统以及无标度网络的详尽模拟，表明振荡器系统的相变可以表现在对底层连接结构的拓扑动力学的时间响应中。
英文摘要：
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such a temporal response. The Kuramoto model under periodically switching interactions has the same type of phase transition as the original mean-field model. Furthermore, we see that the signature of the synchronization transition appears in the relative delay of the order parameter with respect to the phase of oscillating interactions as well. Specifically, the phase shift becomes significantly larger as the system gets closer to the phase transition so that the order parameter at the minimum interaction density can even be larger than that at the maximum interaction density, counterintuitively. We argue that this phase-shift inversion is caused by the diverging relaxation time, in a similar way to the resonance near the critical point in the kinetic Ising model. Our result, based on exhaustive simulations on globally coupled systems as well as scale-free networks, shows that an oscillator system's phase transition can be manifested in the temporal response to the topological dynamics of the underlying connection structure.
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