Synchronization in scale-free dynamical networks: robustness and fragility

By Xiao Fan Wang, Guanrong Chen. 2001

1,150 citations recorded by the source corpus.

Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions are in the power-law form. In this paper, we investigate the synchronization phenomenon in scale-free dynamical networks. We show that if the coupling strength of a scale-free dynamical network is greater than a positive threshold, then the network will synchronize no matter how large it is. We show that the synchronizability of a scale-free dynamical network is robust against random removal of nodes, but is fragile to specific removal of the most highly connected nodes.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Guanrong Chen
2. Wenwu Yu
3. Jinde Cao
4. Wei Ren
5. Jinhu Lu
6. Zidong Wang
7. Jürgen Kurths
8. Z. Duan

In Statistical and Nonlinear Physics

1. Guanrong Chen
2. Wenwu Yu
3. Jinde Cao
4. Jinhu Lu
5. Jürgen Kurths
6. Zidong Wang
7. Tianping Chen
8. Xiaohui Liu

Citations in the corpus

• An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “In synchronization of comp lex networks, the aim is to reveal how the network structure, whi ch is known in priori, affects the nonlinear collective dynami cs [98], [99], while the aim of consensus in multi-agent systems is to figure out how the designed distributed local protocol concerning mobile ”
• Semi-Global Leader-Following Consensus of Linear Multi-Agent Systems With Input Saturation via Low Gain Feedback (2013, background): “Other topics that are highly relevant to consensus are synchronization [4]–[14], swarming [15], [16], flocking [17]–[20] and rendezvous [21].”
• Algebraic Connectivity of Interdependent Networks (2014, background): “In practical terms, this shows that NoN topologies require only a fraction of coupling links in order to achieve optimal diffusivity.”
• Pinning Complex Networks by a Single Controller (2006, methodology): “In [1], [2], th e local stability of the synchronization manifold was studie d via linearization method named “master stability function ”.”
• Local Synchronization of a Complex Network Model (2009, methodology): “Complex networks exist in all fields of sciences and humanities and have been intensively studied over the last few years [1]–[3], [35]–[50].”
• Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay (2006, background): “Thus, c has important engineering and physical sense if we consider the control and physical problem of synchronization [6,11].”
• Distributed Consensus Filtering in Sensor Networks (2009, background): “In [10] and [11], local synchronization was studied based on the transverse stability to the synchronization manifold, where synchronization was discussed with respect to small-world and scale-free network topologies.”
• Robust semi‐global coordinated tracking of linear multi‐agent systems with input saturation (2015, background): “In particular, research on distributed cooperative control protocols has advanced the development of cooperative control in multi-agent systems [3], [4], [5], [6], [7], [8], [9], [10], [11], [12].”
• On pinning synchronization of complex dynamical networks (2009, methodology): “Therefore, a large amount of work has been devoted to the study of synchronization in various largescale complex networks (Cao, Li, & Wang, 2006; W. Lu & T. Chen, 2004; Wang & Cao, 2006; Wang & Chen, 2002a,b; Yu, Cao, & Lü, 2008).”
• Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems (2011, background): “Consider a complex dynamical network consisting of identical nodes with linearly diffusive coupling [17], [27], [29], [31], [32], [35], [37], [38] (6) where is the state vector of the th node, with being a matrix describing the dynamics of each single node, is the inner coupling matrix, and is the…”
• Characterizing the synchronizability of small-world dynamical networks (2004, background): “However, the scale-free networks are more robust against random removal of nodes, but is more fragile to specific removal of the most highly clustering nodes [9].”