Network Reconstruction from Random Phase Resetting

We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random phase resets of the system dynamics. The desired details of network structure are then revealed by appropriately averaging over the ensemble. The method is applicable for a wide class of networks with arbitrary emergent dynamics, including full synchrony.

Figure 1

Four-node network used for illustrating our method.

Figure 2

Reconstruction of network Fig. 1. Circles: Actual parameter values; crosses: numerically obtained values for $I={10}^4$. (Left) $a_{ij}^{(1)}$, (right) $b_{ij}^{(1)}$, for each pair $i\to j$.

Figure 3

Numerical values of $a_{ij}^{(1)}$ for network in Fig. 1, for links [gray (cyan)] and nonlinks (black). (a) Computed from ensemble of $I$ IP (cf. Fig. 2). (b) Computed from $I={10}^4$ for network with attractive interactions, and with resetting done at synchronous state. (c) Computed from $I={10}^5$ for network with attractive interactions where only spikes ($\phi =0$) are observable (see text for more details).