Eur. Phys. J. B 75, 285-297 (2010)
https://doi.org/10.1140/epjb/e2010-00158-6

Pattern evolution in non-synchronizable scale-free networks

¹ Institute for Fusion Theory and Simulation, Zhejiang University, 310027, Hangzhou, P.R. China
² Department of Physics, Zhejiang University, 310027, Hangzhou, P.R. China

Corresponding author: ^a wangxg@zju.edu.cn

Received: 14 January 2010
Revised: 22 April 2010
Published online: 26 May 2010

Abstract

Pattern formation and evolution in the desynchronizing process of scale-free complex networks are investigated. Depending on how far the system is away from the synchronizable regime, two types of synchronous patterns are identified, namely, the giant-cluster state (GCS) and the scattered-cluster state (SCS). GCS is observed when a system is immediately outside of the synchronizable regime, where the dynamics undergoes a process of on-off intermittency and the patterns are signatured by the existence of a giant synchronous cluster. As the system leaves away from the synchronizable regime, GCS gradually transforms into SCS, accompanied by the continuous dissolving of the giant cluster. Both the two types of patterns are non-stationary, reflected as the timely changed size and content of the clusters. By introducing a new form of synchronization, the temporal phase synchronization, we investigate the dynamical and statistical properties of these non-stationary patterns. An interesting finding is that the unstable nodes of GCS, i.e. nodes that escape from the giant cluster more frequently, are independent of the coupling strength but are sensitive to the bifurcation types. The intermittent behavior of GCS is analyzed by a theory of snapshot attractors, and the theoretical predications fit the numerical observations qualitatively well.