Adaptive synchronization of asymmetric coupled networks with multiple coupling delays

Sun, Weiwei; Hao, Fei; Chen, Xia

doi:10.1080/03081079.2012.670856

Cited by 4 publications

(2 citation statements)

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“…Besides, our assumptions are easily satisfied. In a word, our model is more suitable to describe the real‐world networks. Remark When

Δ Γ^{(k)} = 0, k = 2, τ_{1} (t) = τ_{1}

τ_{2} (t) = τ_{2}, ɛ = 1

, the network (1) is translated into

{\overset{x}{true}}_{i} (t) = f (x_{i} (t)) + \sum_{j = 1}^{N} c_{i j}^{(1)} Γ^{(1)} x_{j} (t - τ_{1}) + \sum_{j = 1}^{N} c_{i j}^{(2)} Γ^{(2)} x_{j} (t - τ_{2}), i \in I .

The complex network (27) has been investigated in , which should assume that the inner coupling matrix is positive definite. As a result, we know that this restriction is here relaxed.…”

Section: Resultsmentioning

confidence: 99%

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Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

et al. 2014

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In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015

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“…Besides, our assumptions are easily satisfied. In a word, our model is more suitable to describe the real‐world networks. Remark When

Δ Γ^{(k)} = 0, k = 2, τ_{1} (t) = τ_{1}

τ_{2} (t) = τ_{2}, ɛ = 1

, the network (1) is translated into

{\overset{x}{true}}_{i} (t) = f (x_{i} (t)) + \sum_{j = 1}^{N} c_{i j}^{(1)} Γ^{(1)} x_{j} (t - τ_{1}) + \sum_{j = 1}^{N} c_{i j}^{(2)} Γ^{(2)} x_{j} (t - τ_{2}), i \in I .

The complex network (27) has been investigated in , which should assume that the inner coupling matrix is positive definite. As a result, we know that this restriction is here relaxed.…”

Section: Resultsmentioning

confidence: 99%

“…The complex network (27) has been investigated in [53], which should assume that the inner coupling matrix is positive definite. As a result, we know that this restriction is here relaxed.…”

Section: Remarkmentioning

confidence: 99%