Multistable remote synchronization in a star-like network of non-identical oscillators

•Remote synchronization was found to have strong dependency on initial conditions.•Multistability is numerically reported under intermediate coupling values.•Some initial conditions yield remote synchronization, with quasi periodic motion.•While for some other initial conditions, the system does not converge to synchronized states. In the context of networks of coupled oscillators, remote synchronization happens when phase difference between non-adjacent units become constant, even though there is no global phase-locking. We study such regime considering a star-like network of Stuart-Landau oscillators. As previous works, our setup comprises peripheral nodes with different but close natural frequencies and the central node frequency detuned from them. The main contribution here is to numerically report multistability under intermediate coupling values: some initial condition yield remote synchronization, with quasi-periodic motion; while others do not converge to synchronized states. By using a Gaussian distribution to select the initial phases of the oscillators, we found that relatively small value of the standard deviation and absolute value of the mean of this distribution far from a specific range of values seem to favor remote synchronization in the multistability region. This phenomenon is extensively analyzed for both cases, considering a fixed coupling value.