Synchronization in networks of nonlinear dynamical systems coupled via a directed graph

Wu, Chai Wah

doi:10.1088/0951-7715/18/3/007

Cited by 258 publications

(156 citation statements)

References 19 publications

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“…As pointed out in Ref. [15], the connectivity of the graph plays a significant role for chaos synchronization.…”

Section: Introductionmentioning

confidence: 93%

“…It can be described by the threshold of the coupling strength to guarantee that the coupled system can synchronize. For complete synchronization, it was formulated as a function of the eigenvalues of symmetric Laplacian [11] or certain Rayleigh quotient of asymmetric Laplacian [15]. How the topology of the underlying graph affects synchronizability is an important issue for the study of complex networks [2].…”

Section: A Clustering Synchronizabilitymentioning

confidence: 99%

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Cluster synchronization in networks of coupled nonidentical dynamical systems

Lu¹,

Liu²,

Chen³

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

199

132

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In this paper, we study cluster synchronization in networks of coupled non-identical dynamical systems.The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two condition play key roles for cluster synchronization: the common inter-cluster coupling condition and the intra-cluster communication. From the latter one, we interpret the two well-known cluster synchronization schemes: self-organization and driving, by whether the edges of communication paths lie at interor intra-cluster. By this way, we classify clusters according to whether the set of edges inter-or intra-cluster edges are removable if wanting to keep the communication between pairs of vertices in the same cluster.Also, we propose adaptive feedback algorithms on the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the two conditions above. We also give several numerical examples to illustrate the theoretical results.

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“…As pointed out in Ref. [15], the connectivity of the graph plays a significant role for chaos synchronization.…”

Section: Introductionmentioning

confidence: 93%

Section: A Clustering Synchronizabilitymentioning

confidence: 99%

Cluster synchronization in networks of coupled nonidentical dynamical systems

Lu¹,

Liu²,

Chen³

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

199

132

View full text Add to dashboard Cite

show abstract

“…However, for regular networks such as rings, topics such as synchronization and bifurcations are studied (Kaneko, 1985;Wu, 2005). As discussed earlier, the effects of changes in a network by edge rewirings on epidemic properties are investigated (Eubank, 2010;Chen, 2010).…”

Section: Related Workmentioning

confidence: 99%

Sensitivity of Diffusion Dynamics to Network Uncertainty

Adiga¹,

Kuhlman²,

Mortveit³

et al. 2014

jair

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Simple diffusion processes on networks have been used to model, analyze and predict diverse phenomena such as spread of diseases, information and memes. More often than not, the underlying network data is noisy and sampled. This prompts the following natural question: how sensitive are the diffusion dynamics and subsequent conclusions to uncertainty in the network structure?In this paper, we consider two popular diffusion models: Independent cascade (IC) model and Linear threshold (LT) model. We study how the expected number of vertices that are influenced/infected, for particular initial conditions, are affected by network perturbations. Through rigorous analysis under the assumption of a reasonable perturbation model we establish the following main results. (1) For the IC model, we characterize the sensitivity to network perturbation in terms of the critical probability for phase transition of the network. We find that the expected number of infections is quite stable, unless the transmission probability is close to the critical probability. (2) We show that the standard LT model with uniform edge weights is relatively stable under network perturbations. (3) We study these sensitivity questions using extensive simulations on diverse real world networks and find that our theoretical predictions for both models match the observations quite closely. (4) Experimentally, the transient behavior, i.e., the time series of the number of infections, in both models appears to be more sensitive to network perturbations.

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“…Indeed, it is always possible to choose an S having as few as two vertices and containing no directed spanning tree. Since the resulting graph G also contains no directed spanning tree, it is incapable of chaotic synchronization [32].…”

Section: Structural Limitations To Synchronizationmentioning

confidence: 99%

Network synchronization: Spectral versus statistical properties

Atay

Bıyıkoğlu

Jost

2006

Physica D: Nonlinear Phenomena

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We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks.

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Synchronization in networks of nonlinear dynamical systems coupled via a directed graph

Cited by 258 publications

References 19 publications

Cluster synchronization in networks of coupled nonidentical dynamical systems

Cluster synchronization in networks of coupled nonidentical dynamical systems

Sensitivity of Diffusion Dynamics to Network Uncertainty

Network synchronization: Spectral versus statistical properties

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