Adaptive Synchronization of an Uncertain Complex Dynamical Network

Zhou, Jin; Lu, Jun-an; Lü, Jinhu

doi:10.1109/tac.2006.872760

Cited by 631 publications

(334 citation statements)

References 19 publications

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“…[5][6][7][8][9][10][11][12] In particular, adaptive techniques, have emerged as an exciting research topic in nonlinear system control, and have been demonstrated to be an effective way to synchronize a complex network. [8][9][10] However, it is assumed that all the nodes need to be controlled. In view of impracticality of controlling all the nodes in a large-scale network, pinning control has been introduced in recent years.…”

Section: X In ͑T͒͒mentioning

confidence: 99%

Pinning synchronization of delayed neural networks

Zhou

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates adaptive pinning synchronization of a general weighted neural network with coupling delay. Unlike recent works on pinning synchronization which proposed the possibility that synchronization can be reached by controlling only a small fraction of neurons, this paper aims to answer the following question: Which neurons should be controlled to synchronize a neural network? By using Schur complement and Lyapunov function methods, it is proved that under a mild topology-based condition, some simple adaptive feedback controllers are sufficient to globally synchronize a general delayed neural network. Moreover, for a concrete neurobiological network consisting of identical Hindmarsh–Rose neurons, a specific pinning control technique is introduced and some numerical examples are presented to verify our theoretical results.

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Section: X In ͑T͒͒mentioning

confidence: 99%

Pinning synchronization of delayed neural networks

Zhou

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Chen and Zhou [10] studied synchronization of general complex networks via the adaptive feedback control scheme. Zhou, Lu and Lü [11] investigated locally and globally adaptive synchronization of an uncertain complex dynamical network. For other relevant results, we refer the readers to Refs.…”

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confidence: 99%

Synchronization in an array of linearly stochastically coupled networks with time delays

Cao

Wang

Sun

2007

Physica A: Statistical Mechanics and its Applications

210

106

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In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays.Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.

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“…During the past few years, complex networks have become an interesting research topic and appeal to have more attention in different fields from mathematics, biology, engineering sciences (Osborn 2010;Kamel and Xia 2009;Zhang et al 2013e, 2014bWatts and Strogatz 1998;Barabasi and Albert 1999;Zhou et al 2006;Strogatz 2001;Lü and Chen 2005). A complex network is a large set of interconnected nodes, where the nodes and connections can be anything, examples are internet, transportation networks, coupled biological and chemical engineering systems, neural networks in human brains and so on.…”

Section: Introductionmentioning

confidence: 99%

Event-based exponential synchronization of complex networks

2016

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In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed eventtriggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.

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Adaptive Synchronization of an Uncertain Complex Dynamical Network

Cited by 631 publications

References 19 publications

Pinning synchronization of delayed neural networks

Pinning synchronization of delayed neural networks

Synchronization in an array of linearly stochastically coupled networks with time delays

Event-based exponential synchronization of complex networks

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