Reconstruction of a random phase dynamics network from observations

Abstract

We consider networks of coupled phase oscillators of different complexity: Kuramoto-Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.

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• The Role of Data in Model Building and Prediction: A Survey Through Examples
• A practical method for estimating coupling functions in complex dynamical systems
• Recovering sparse networks: Basis adaptation and stability under extensions
• Impact of network characteristics on network reconstruction
• High-Order Phase Reduction for Coupled Oscillators
• Data assimilation for networks of coupled oscillators: Inferring unknown model parameters from partial observations
• Distinguishing pairwise and higher-order interactions in coupled oscillators from time series