Synchronization in discrete-time networks with general pairwise coupling

Abstract

We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed transverse exponents and derive sufficient conditions for local complete synchronization. The general non-diffusive coupling scheme can lead to new synchronous behavior, in networks of identical units, that cannot be produced by single units in isolation. In particular, we show that synchronous chaos can emerge in networks of simple units. Conversely, in networks of chaotic units simple synchronous dynamics can emerge; that is, chaos can be suppressed through synchrony.

References in corpus (5)

• Synchronization in complex networks
• Delays, connection topology, and synchronization of coupled chaotic maps
• Spectral Properties and Synchronization in Coupled Map Lattices
• Synchronization of discrete-time dynamical networks with time-varying couplings
• Synchronized chaos in networks of simple units

Cited by in corpus (5)

• Synchronized chaos in networks of simple units
• Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian
• Symbolic dynamics and synchronization of coupled map networks with multiple delays
• Analytic relationship of relative synchronizability to network structure and motifs
• Covering relations for coupled map networks