Synchronization is Enhanced in Weighted Complex Networks

Chávez, Mario; Hwang, Dong‐Uk; Amann, Andreas; Hentschel, H. G. E.; Boccaletti, Stefano

doi:10.1103/physrevlett.94.218701

Cited by 439 publications

(301 citation statements)

References 18 publications

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“…Motivated by the practical requirement and theoretical interest, numbers of scientists begin to study how to enhance the network synchronizability, especially for scalefree networks [41,42]. These methods keep the network topology unchanged, while add some weight into the system, thus the coupling matrix is changed.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Enhanced synchronizability by structural perturbations

et al. 2005

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In this paper, we investigate the collective synchronization of system of coupled oscillators on Barabási-Albert scale-free network. We propose an approach of structural perturbations aiming at those nodes with maximal betweenness. This method can markedly enhance the network synchronizability, and is easy to be realized. The simulation results show that the eigenratio will sharply decrease to its half when only 0.6% of those hub nodes are under 3-division processes when network size N = 2000. In addition, the present study also provides a theoretical evidence that the maximal betweenness plays a main role in network synchronization.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Enhanced synchronizability by structural perturbations

et al. 2005

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“…[6][7][8][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In particular, the study on controlling the dynamics of a network and guiding it to a desired state, such as, an equilibrium point or a periodic orbit of the network has become an interesting and important direction in this research field. 7,[18][19][20][22][23][24]26,27 It has been revealed that, in the process of controlling various networks, feedback control serves as a simple and effective approach for stabilization and synchronization.…”

Section: Introductionmentioning

confidence: 99%

Pinning control of fractional-order weighted complex networks

Tang

Wang

Fang

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

129

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In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3068350͔Recently, fractional-order differential systems have been widely investigated due to their potential applications in viscoelasticity, dielectric polarization, quantum evolution of complex systems, and many other fields. On the other hand, research of complex networks has triggered tremendous interest during the past decade. Most studies to date have concerned integer-order complex networks. In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The fractional-order complex networks generalize wellstudied integer-order complex networks. Some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated by utilizing the eigenvalue analysis and fractional-order stability theory. A surprising finding that the fractional-order networks can stabilize itself by reducing the fractional-order q without pinning any node is presented. The numerical algorithms for fractional-order networks are also presented. In the end, computer simulations in scale-free networks are given to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger coupling strength c, the more capacity that the pinning strategy can possess to accelerate the control rate of fractional-order networks.

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“…In the last two decades dynamics on network received a growing amount of interest [Dhamala et al, 2004;Zigzag et al, 2009;Choe et al, 2010;Chavez et al, 2005;Sorrentino and Ott, 2007;Albert et al, 2000;Kinzel et al, 2009;Lehnert et al, 2011a;Keane et al, 2012]. One of the central topics of dynamics on networks is synchronization [Strogatz and Stewart, 1993;Rosenblum et al, 1996;Pikovsky et al, 2001;Pecora and Carroll, 1998;Mosekilde et al, 2002;Wang and Chen, 2002;Arenas et al, 2006aArenas et al, , 2008Balanov et al, 2009;Omelchenko et al, 2010;Schöll, 2013].…”

Section: Dynamics On Networkmentioning

confidence: 99%

“…Previous research in the field of network science focused either on the construction of topologies [Rapoport, 1957;Erdős and Rényi, 1959;Watts and Strogatz, 1998;Albert and Barabasi, 2002;Newman, 2003;Boccaletti et al, 2006b] or on the dynamics on a network with fixed topology Dhamala et al, 2004;Chavez et al, 2005;Sorrentino and Ott, 2007;Zigzag et al, 2009;Choe et al, 2010;Kinzel et al, 2009;Lehnert et al, 2011a;Keane et al, 2012]. Recently, adaptive networks attracted a lot of interest as they bring these two aspects together: In such networks the topology evolves according to the state of the system while the dynamics on the network and thus the state is influenced by the topology [Gross and Blasius, 2008].…”

Section: Adaptive Networkmentioning

confidence: 99%

“…In the field of complex networks, topological features enhancing or weakening synchronizability are of great interest [Pecora and Carroll, 1998;Chavez et al, 2005;Lehnert et al, 2011a;Keane et al, 2012]. Here, we discuss the structural properties of the networks after successful control, in order to elucidate the common features that enable synchronization in a cluster state.…”

Section: Structural Propertiesmentioning

confidence: 99%

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Controlling Synchronization Patterns in Complex Networks

Lehnert¹

2016

Springer Theses

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In this thesis, I consider the control of synchronization in delay-coupled complex networks. As one main focus, several applications to neural networks will be discussed. In the first part, I focus on the stability of synchronization in complex networks meaning that the control is realized by considering the stability of synchrony in dependence on the parameters. In the second part, adaptive control of synchronization is studied. To this end, adaptive control algorithms are developed that tune the system parameters such that the desired control goal is reached.Besides zero-lag synchrony -a state where all nodes follow the same dynamics without a phase lag -groups and cluster states are considered, i.e., states where the network consists of several groups where the nodes within one group are in zero-lag synchrony and, in the case of cluster synchrony, with a constant phase lag between the clusters.The stability of synchronization can be accessed via the master stability function [Pecora and Carroll, 1998]. This convenient tool allows for treating the node dynamics and the network topology in two separate steps, and, thus, allows for a quite general treatment of different network topologies. In this thesis, I will discuss the generalization of the master stability function to group and cluster states and to non-smooth systems.The master stability function can be used to investigate synchrony in neural networks. Neurons are excitable systems where type-I and type-II excitability can be distinguished. Here, the stability of synchrony for both types in complex networks with excitatory and inhibitory links is investigated on two generic models, namely the normal form of the saddle-node infinite period bifurcation and the FitzHugh-Nagumo system. Furthermore, synchronization in systems with heterogeneous delays or node parameters is studied.In situations where parameters are unknown or drift, adaptive control methods are useful since they allow for an automatically realized adaption of the control parameters. A convenient adaptive method is the speed-gradient method that minimizes a predefined goal function [Fradkov, 1979[Fradkov, , 2007. I first apply this method in the control of an unstable focus and an unstable periodic orbit embedded in the Rössler attractor. Furthermore, I show that clusters states in networks of delayed coupled Stuart-Landau oscillators can be controlled by adaptively tuning the phase of the complex coupling strength or by adapting the topology. The first method is particularly simple because only one parameter has to be adapted, while the second method is more reliable in the sense that its success is widely independent of the choice of the control parameters and the initial conditions. ZUSAMMENFASSUNGIn dieser Arbeit wird die Kontrolle von Synchronisation in komplexen Netzwerken mit retardierten Kopplungen untersucht. Dabei werden verschiedene Anwendungen auf neuronale Netzwerke diskutiert. Der erste Teil der Arbeit beschäftigt sich mit der Stabilität von Synchronisation in komplexen Ne...

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Synchronization is Enhanced in Weighted Complex Networks

Cited by 439 publications

References 18 publications

Enhanced synchronizability by structural perturbations

Enhanced synchronizability by structural perturbations

Pinning control of fractional-order weighted complex networks

Controlling Synchronization Patterns in Complex Networks

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