Blinking model and synchronization in small-world networks with a time-varying coupling

Belykh, Igor; Белых, В. Н.; Hasler, M.

doi:10.1016/j.physd.2004.03.013

Cited by 335 publications

(237 citation statements)

References 36 publications

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“…To obtain a sufficient condition, one can use global stability analysis, like Lyapunov's direct method (Belykh et al, 2006(Belykh et al, , 2005(Belykh et al, , 2004aChen, 2006Chen, , 2008Li et al, 2009;Chua, 1994, 1995a,b,c) or contraction theory (Aminzare and Sontag, 2015;Li et al, 2007;Lohmiller and Slotine, 1998;Pham and Slotine, 2007;Russo and Di Bernardo, 2009;Tabareau et al, 2010;Wang and Slotine, 2005).…”

Section: Master Stability Formalism and Beyondmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Section: Master Stability Formalism and Beyondmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

View full text Add to dashboard Cite

show abstract

“…Future efforts will be devoted to investigate the upper bound of degree d y and d θ to ensure the robust synchronization. In addition, particular interests have casted on stochastic synchronization with randomly switching topology, like representative stochastic models used in [15], [16], [18].…”

Section: Discussionmentioning

confidence: 99%

“…Time-varying networks can also be modelled by stochastic switching networks [15]- [19]. In [15], a connection graph stability method, also proposed by [20], is extended to a blinking model of small-world network in which both fixed 2K-nearest neighbor coupling and time-dependent on-off coupling are considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [15], a connection graph stability method, also proposed by [20], is extended to a blinking model of small-world network in which both fixed 2K-nearest neighbor coupling and time-dependent on-off coupling are considered. In [16], each agent is assumed to be a random walker and random changes of network can be described by the change of agents' locations in the lattice where information can be transmitted only for agents in the same lattice.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Han

Chesi

2014

IEEE Trans. Circuits Syst. I

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Abstract-Robust synchronization problem is a key issue in chaotic circuits and nonlinear systems. This paper is concerned with robust synchronization problem of polynomial nonlinear system affected by time-varying uncertainties on topology, i.e., structured uncertain parameters constrained in a boundedrate polytope. Via partial contraction analysis, novel conditions, both for robust exponential synchronization and for robust asymptotical synchronization, are proposed by using parameterdependent contraction matrices. In addition, for polynomial nonlinear system, this paper introduces a new class of contraction matrix, i.e., homogeneous parameter-dependent polynomial contraction matrix (HPD-PCM), by which tractable conditions of linear matrix inequalities (LMIs) are provided via affine space parametrizations. Furthermore, the variant rate margin for robust asymptotical synchronization is, for the first time, proposed and investigated via handling generalized eigenvalue problems (GEVPs). A set of representative examples demonstrate the effectiveness of proposed method.

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“…While the influences of the network structure on dynamics have been intensively studied in the past [3], recently attentions have also been paid to the influences of the network dynamics on structure, i.e. the evolution of complex networks driven by dynamics [4,5,6,7,8,9,10]. In Ref.…”

mentioning

confidence: 99%

Evolution of functional subnetworks in complex systems

Wang

Lai

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved and developed according to the network structure and dynamics. In particular, we study the case of evolutionary clustered networks in which the function of each link (either attractive or repulsive coupling) is updated by the local dynamics. It is found that, during the process of system evolution, the network is gradually stabilized into a particular form in which the attractive (repulsive) subnetwork consists only the intralinks (interlinks). Based on the properties of subnetwork evolution, we also propose a new algorithm for network partition which is distinguished by the convenient operation and fast computing speed. The past decade has witnessed the blooming of network science, in which one important issue is to explore the interplay between the network structure and dynamics [1,2]. While the influences of the network structure on dynamics have been intensively studied in the past [3], recently attentions have also been paid to the influences of the network dynamics on structure, i.e. the evolution of complex networks driven by dynamics [4,5,6,7,8,9,10]. In Ref.[5] it has been shown that, rewiring network links according to the node synchronization, a random network can be gradually developed to a smallworld network. In Ref. [7] it has been shown that, driven by node synchronization, the weight of the network links can be developed to a particular form in favor of global network synchronization. Besides network evolution, dynamics has been also used for network detection, e.g., detecting the modular structures in clustered complex networks [6,7,8,9,10,11].It has been well recognized that links in a practical network are usually different from each other. In previous studies, this has been mainly reflected in the variation of the weight of the network links, i.e., the weighted network [1]. Weighted network, however, describes only the case of single-function networks, i.e. all links in the network have the same function, but failing to describe the situation of multi-function networks in which the network links have the diverse functions. A type of commonly seen multi-function networks in practice is the cooperation-competition network (CCN) [12,13], in which the network links are divided into two groups of opposite functions. For instance, in the nervous network of the human brain, the synapses are roughly divided into two groups, excitatory and inhibitory, which play the contrary roles to the neuron activities [12]. Another typical example of CCN is the relationship network shown in the prisoner's dilemma game, in which each suspect may either cooperate with (remain silent) or defect from (betray) the other suspects [13]. * Corresponding author. Email address: wangxg@zju.edu.cn For multi-function networks like CCN, to facilitate the analysis, it will be convenient if we tr...

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Blinking model and synchronization in small-world networks with a time-varying coupling

Cited by 335 publications

References 36 publications

Control principles of complex systems

Control principles of complex systems

Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Evolution of functional subnetworks in complex systems

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