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Real-world complex systems such as ecological communities and neuron networksare essential parts of our everyday lives. These systems are composed of unitswhich interact through intricate networks. The ability to predict suddenchanges in network behaviour, known as critical transitions, from data isimportant to avert disastrous consequences of major disruptions. Predictingsuch changes is a major challenge as it requires forecasting the behaviour forparameter ranges for which no data on the system is available. In this paper,we address this issue for networks with weak individual interactions andchaotic local dynamics. We do this by building a model network, termed aneffective network, consisting of the underlying local dynamics at each node anda statistical description of their interactions. We illustrate this approach byreconstructing the dynamics and structure of realistic neuronal interactionnetworks of the cat cerebral cortex. We reconstruct the community structure byanalysing the stochastic fluctuations generated by the network and predictcritical transitions for coupling parameters outside the observed range.

Effective networks: a model to predict network structure and critical transitions from datasets