标题： 动态网络中的内部可靠性与反可靠性 显示英文标题

标题： Internal reliability and anti-reliability in dynamical networks

摘要： 我们考虑有限动态网络，并根据复制单元或一组单元的同步特性定义内部可靠性。 如果复制单元的状态与其原型一致，它们是可靠的；否则，如果它们的状态不同，则是反可靠的。 通过横向李雅普诺夫指数量化可靠性，可以对不同模型进行直接分析。 对于具有自然频率分布的全局耦合相位振子的库伦托模型，我们表明在同步开始之前，频率外围的单元是反可靠的，而中心的单元是可靠的。 对于此模型，可靠性可以通过相位相关性以某种涨落-耗散关系表达。 库伦托模型中足够大的子网络总是反可靠的；同样，对于递归神经网络，个体单元总是可靠的。 显示英文摘要

摘要： We consider finite dynamical networks and define internal reliability according to the synchronization properties of a replicated unit or a set of units. If the states of the replicated units coincide with their prototypes, they are reliable; otherwise, if their states differ, they are anti-reliable. Quantification of reliability with the transversal Lyapunov exponent allows for a straightforward analysis of different models. For a Kuramoto model of globally coupled phase oscillators with a distribution of natural frequencies, we show that prior to the onset of synchronization, peripheral in frequency units are anti-reliable, while central are reliable. For this model, reliability can be expressed via phase correlations in a sort of a fluctuation-dissipation relation. Sufficiently large sub-networks in the Kuramoto model are always anti-reliable; the same holds for a recurrent neural network, where individual units are always reliable.