2016/01/06 by Yafeng Wang, Wang, Yafeng, Huawei Fan +5
Computer Science · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1601.01052
openalex publication_date 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands or grows. A network in the real world can never be completely synchronized due to noise and/or external disturbances. This is especially the case when, mathematically, the transient synchronous state during the growth process becomes marginally stable, as a local perturbation can trigger a rapid deviation of the system from the vicinity of the synchronous state. In terms of the nodal dynamics, a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverge from the synchronous state in a cascading manner within a short time period. Because of the high dimensionality of the networked system, the transient process for the system to recover to the synchronous state can be extremely long. Introducing a tolerance threshold to identify the desynchronized nodes, we find that, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis indicates that, the distribution of the size of the collapse is approximately algebraic (power law), regardless of the fluctuations in the system parameters. This is indication of the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.