Dynamics of slow and fast systems on complex networks

Abstract

We study the occurrence of frequency synchronized states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network, where out of N systems, m evolve on a slower time scale. In such systems, in addition to frequency synchronized states, we also observe amplitude death, synchronized clusters and multifrequency states. We report an interesting crossover behavior from fast to slow collective dynamics as the number of slow systems m increases. The transition to amplitude death is analyzed in detail for minimal network configurations of 3 and 4 systems which actually form possible motifs of the full network.