Synchronization of machine learning oscillators in complex networks.

We study synchronization phenomena in complex networks in terms of machine learning oscillators without conventional dynamical equations. Specifically, we adopt an effective machine learning technique known as reservoir computing for modeling dynamical systems of interest. By constructing a coupled configuration, we show that a collection of coupled reservoir oscillators are in identical synchrony over a wider window of coupling strengths. We find that the geometrical and dynamical properties of synchronous orbits are in excellent agreement with that of the learned dynamical system. Remarkably, through this synchronization scheme, we successfully recover an almost identical bifurcation behavior of an observed system via merely its chaotic dynamics. Our work provides an alternative framework for studying synchronization phenomena in nature when only observed data are available.