Graph-theoretic approach to exponential synchronization of coupled systems on networks with mixed time-varying delays

Guo, Beibei; Xiao, Yu; Zhang, Chiping

doi:10.1016/j.jfranklin.2017.05.029

Cited by 14 publications

(11 citation statements)

References 31 publications

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“…Remark In Theorem , we construct the global Lyapunov function as

V false(t false) = \sum_{k = 1}^{n} c_{k} d_{k} V_{k} false(t false)

, where weights c k and d k are the cofactors of the k th diagonal element of

{scriptL}_{\overset{A}{true}}

and

{scriptL}_{\overset{B}{true}}

, respectively, which shows that the exponential stability of the trivial solution of system has a close relationship with the topological structure of the coupled network. This kind of construction was first proposed by Li et al and was applied to many other systems successfully . Theorem extends this construction to CSNs with multicoupling structure.…”

Section: Global Stability Analysismentioning

confidence: 87%

“…Remark In fact, the assumption on the strong connectedness of considered coupled networks is common . If the strong connectedness is not satisfied, only a part of vertices' stability can be promised (see remark 3 in the work of Li et al for a detailed explanation).…”

Section: Global Stability Analysismentioning

confidence: 99%

“…These make the model more practical. On one hand, compared with other works, [5][6][7][8][9][10][11][12][13][14] we consider one more coupling structure, which makes our model more general because related works 5-14 cannot deal with the example in Section 2.2. On the other hand, although many literature considered the practical models such as neural networks model [17][18][19][23][24][25][26][27] that involve two coupling structures, the coupling structure was taken as H kh (x h ), which is independent of x k .…”

Section: Model Formulationsmentioning

confidence: 99%

“…In 2010, Li et al first explored the stability of CSNs by means of the Lyapunov method and graph‐theoretical technique. After that, based on the work of Li and Shuai, many interesting results were reported for more general CSNs, such as the stability of stochastic CSNs, the stability of complex‐valued CSNs, and the synchronization of CSNs . However, it should be pointed out that the aforementioned works only consider CSNs with single coupling.…”

Section: Introductionmentioning

confidence: 99%

“…After that, based on the work of Li and Shuai, 5 many interesting results were reported for more general CSNs, such as the stability of stochastic CSNs, 6-9 2364 2365 the stability of complex-valued CSNs, 10,11 and the synchronization of CSNs. [12][13][14][15][16] However, it should be pointed out that the aforementioned works only consider CSNs with single coupling. This kind of CSNs will restrict the study of many real-world applications.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Wang

Sun

Fan

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper explores the stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays (ICSNMT). The coupling structure can be nonlinear and the time‐varying delays in which can be different, which can well describe more realistic networks. In order to describe this multicoupling structure, we build ICSNMT on a digraph with multiple arcs. Two cases are discussed, ie, (i) the continuous dynamics is stable and (ii) the impulsive dynamics is stable. Then, by means of impulsive differential inequalities with multiple delays and weighted Lyapunov functions method where the weights are closely linked to the network's topological structure, some stability criteria are established. Then, the theoretical results are illustrated by examples of bidirectional associative memory neural networks and coupled modified Chua's circuits, respectively. The numerical simulations are also carried out to demonstrate the effectiveness and feasibility of our theoretical findings.

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“…Remark In Theorem , we construct the global Lyapunov function as

V false(t false) = \sum_{k = 1}^{n} c_{k} d_{k} V_{k} false(t false)

, where weights c k and d k are the cofactors of the k th diagonal element of

{scriptL}_{\overset{A}{true}}

and

{scriptL}_{\overset{B}{true}}

Section: Global Stability Analysismentioning

confidence: 87%

Section: Global Stability Analysismentioning

confidence: 99%

Section: Model Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Wang

Sun

Fan

et al. 2019

Intl J Robust & Nonlinear

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Stability and synchronization of fractional‐order delayed multilink complex networks with nonlinear hybrid couplings

Wang

et al. 2020

Math Methods in App Sciences

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In this paper, the stability and synchronization problems of fractional‐order delayed multilink complex networks with nonlinear hybrid couplings are investigated simultaneously, where discrete time‐varying delays and distributed time‐varying delays are both taken into account. By virtue of graph‐theoretic approach and Lyapunov method, under feedback control, some criteria are established to guarantee that the underlying networks achieve stability and synchronization. The obtained criteria are related to topological structure of subsystems, control gain, and the upper bound of time‐varying delays. Furthermore, in order to show practicality, the obtained results are applied to fractional‐order delayed multilink competitive neural networks with nonlinear hybrid couplings and fractional‐order Lorenz chaotic delayed coupled systems with nonlinear hybrid couplings, respectively. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of our theoretical results.

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Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

Wang

2018

Nonlinear Dyn

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Graph-theoretic approach to exponential synchronization of coupled systems on networks with mixed time-varying delays

Cited by 14 publications

References 31 publications

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Stability and synchronization of fractional‐order delayed multilink complex networks with nonlinear hybrid couplings

Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

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