Small-world networks exhibit pronounced intermittentsynchronization

We report the phenomenon of temporally intermittently synchronized and desynchronizeddynamics in Watts-Strogatz networks of chaotic Rössler oscillators. We consider topologiesfor which the master stability function (MSF) predicts stable synchronized behaviour, asthe rewiring probability (p) is tuned from 0 to 1. MSF essentiallyutilizes the largest non-zero Lyapunov exponent transversal to the synchronizationmanifold in making stability considerations, thereby ignoring the other Lyapunovexponents. However, for an N-node networked dynamical system, we observethat the difference in its Lyapunov spectra (corresponding to the N – 1directions transversal to the synchronization manifold) is crucial and serves as anindicator of the presence of intermittently synchronized behaviour. In addition to thelinear stability-based (MSF) analysis, we further provide global stability estimate interms of the fraction of state-space volume shared by the intermittently synchronizedstate, as p is varied from 0 to 1. This fraction becomes appreciablylarge in the small-world regime, which is surprising, since this limithas been otherwise considered optimal for synchronized dynamics. Finally, we characterizethe nature of the observed intermittency and its dominance in state-space as networkrewiring probability (p) is varied.