Reconstruction of coupling structure in network of neuron-like oscillators based on a phase-locked loop

Abstract We study the problem of reconstructing the model equations for the network of 3rd order neuron-like oscillators from time series. The nodes of the network are phase-locked loop systems, which are able to exhibit different dynamical regimes including quasiharmonic oscillations, spiking, bursting, and chaotic behavior. Different network topologies are considered, including star, ring, chain, and random architectures. A special approach using the idea of node nonlinear function continuity for constructing the target function is applied, which allows to reduce the model parametrization. Both the coupling parameters and parameters of individual nodes are estimated. Methods for the automatic noise reduction and superfluous coupling term removal are suggested and verified. These approaches provide a possibility to reconstruct the network topology even in the presence of a 10% measurement noise from the single scalar observable from each node in the case of different dynamical regimes and coupling architectures. This can find practical applications in neuroscience, in particular, for network reconstruction from experimental signals of individual cells.