Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

中文翻译：

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从数据揭示动态，社区和重要性

诸如生态群落和神经元网络之类的复杂系统是我们日常生活的重要组成部分。这些系统由通过复杂网络交互的单元组成。从数据预测这些网络动态变化的能力（称为关键过渡）对于避免重大破坏的灾难性后果非常重要。预测此类变化是一项重大挑战，因为它需要预测系统上没有可用数据的参数范围的行为。我们针对个体互动薄弱且局部动力学混乱的网络解决此问题。为此，我们建立了一个模型网络（称为有效网络），该模型网络由基础的局部动力学及其相互作用的统计描述组成。我们表明，此类网络的行为可以根据紧急确定性成分和波动项进行分解。传统上，此类波动会被滤除。但是，正如我们所示，它们是访问交互结构的关键。我们在猫大脑皮层的现实神经元相互作用网络的合成时间序列和光电振荡器的实验多元数据上说明了这种方法。我们通过分析网络产生的随机波动来重建社区结构，并预测耦合参数超出观察范围的临界转变。我们在猫大脑皮层的现实神经元相互作用网络的合成时间序列以及光电振荡器的实验多元数据上说明了这种方法。我们通过分析网络产生的随机波动来重建社区结构，并预测耦合参数超出观察范围的临界转变。我们在猫大脑皮层的现实神经元相互作用网络的合成时间序列和光电振荡器的实验多元数据上说明了这种方法。我们通过分析网络产生的随机波动来重建社区结构，并预测耦合参数超出观察范围的临界转变。