Rosin David P, Rontani Damien, Haynes Nicholas D, Schöll Eckehard, Gauthier Daniel J
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin D-10623, Germany.
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Supélec, OPTEL Research Group and LMOPS EA-4423, 2 Rue Edouard Belin, Metz F-57070, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):030902. doi: 10.1103/PhysRevE.90.030902. Epub 2014 Sep 30.
We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.
我们研究了非局部耦合电子振荡器网络，这些网络可以用类似Kuramoto的模型进行近似描述。实验网络在从随机初始条件到网络同步的过程中表现出长时间的复杂瞬态。这些瞬态呈现出复杂的行为，包括奇异态的重现，奇异态是一种有序和无序共存的网络动力学。奇异态的空间域在网络中移动，并与去同步动力学交替出现。我们的振荡器的快速时间尺度（约为100纳秒）使我们能够研究由一百多个节点组成的大型网络的瞬态时间的标度，这在之前的实验中尚未得到证实，并且在许多自然网络中可能具有潜在的重要性。我们发现，平均瞬态时间随网络规模呈指数增长，并且在实验和模拟中都可以建模为泊松过程。这种指数标度是同步速率遵循相空间体积幂律的结果。
