The synchronization of complex dynamical networks with similar nodes and coupling time-delay

Fan, Yongqing; Wang, Yinhe; Zhang, Yun; Wang, Qinruo

doi:10.1016/j.amc.2013.01.013

Cited by 21 publications

(26 citation statements)

References 24 publications

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“…. , N ), which means that the time-varying complex dynamical network (6) realizes asymptotic synchronization with the decentralized controllers (20). This completes the proof of Theorem 2.…”

Section: Remarkmentioning

confidence: 65%

“…Suppose that the OCCCB δ = 10 is known in advance. For this case, we can apply the controllers (20) in Theorem 2 to synchronize the network (6). Here change η to 50.…”

Section: Numerical Simulationsmentioning

confidence: 98%

“…A complex dynamical network with different dimensional similar nodes will exhibit much more complicated behaviors than those with the nodes of the same state dimension. Although [19][20][21] designed the synchronization controllers for the complex dynamical networks with different dimensional similar nodes, all of them did not put the time-varying topology structure and non-dissipatively coupled nodes into consideration.…”

Section: Introductionmentioning

confidence: 99%

“…Generally speaking, each node has other different characters except for the common quality which is named as similarity. Therefore, it is reasonable to character the similarity of the nodes in these networks via the dynamics of each node as did in [19][20][21], no matter whether their state dimensions are different or not. A complex dynamical network with different dimensional similar nodes will exhibit much more complicated behaviors than those with the nodes of the same state dimension.…”

Section: Introductionmentioning

confidence: 99%

“…By using pinning control method, the cluster synchronization problem for the time-varying delays coupling networks was investigated and some useful cluster synchronization criteria were derived in [2]. Decentralized linear controllers and linear matrix inequalities were used to realize the synchronization of complex dynamical networks with different dynamics of nodes in [19,20]. Decentralized dynamical compensation controllers were synthesized to guarantee the asymptotic synchronization of complex dynamical networks with nonlinear nodes of different dimensions and nonlinear coupling functions in [21].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

2015

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This paper investigates the synchronization problem for the non-dissipatively coupled timevarying complex dynamical networks via decentralized state feedback controllers. In our network model, the outer coupling configuration matrices are not restricted by dissipatively coupled condition, time invariance, symmetry, irreducibility or certainty. Besides, different time-varying coupling delays are put into consideration. Moreover, the similarities possessed by the nodes in our network model are revealed based on the nodes' dynamics and are applied to synthesize the controllers. Furthermore, it is the common bound, not the exact information, of the outer coupling coefficients that is used to design the synchronization controllers. It is worth pointing out that the uncertain outer coupling coefficients' common bound is admissible in our synchronization schemes, and for this case, adaptive control mechanism is introduced to design the synchronization controllers. Several proper simulation examples are given to verify the effectiveness and feasibility of our theoretical results.

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Section: Remarkmentioning

confidence: 65%

“…Suppose that the OCCCB δ = 10 is known in advance. For this case, we can apply the controllers (20) in Theorem 2 to synchronize the network (6). Here change η to 50.…”

Section: Numerical Simulationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

2015

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Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller

Zhang

Wang

et al. 2019

Asian Journal of Control

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This paper investigates the generalized projective synchronization (GPS) among the nodes within a complex dynamical network (CDN). Multiple characteristics of realistic networks are simultaneously considered in our network model. First, one crucial node is introduced into our CDN, which behaves like a leader and exists in many practical networks. Second, the commonalities between the crucial node and every other node are discussed and they are embodied in the network model. Third, our CDN is composed of different dimensional nodes and has an overall time‐varying coupling strength. Furthermore, in order to describe more synchronous phenomena, the exponential generalized projective synchronization (EGPS) and asymptotic generalized projective synchronization (AGPS) are defined. The main objective of this paper is to design an effective but simple decentralized controller for the crucial node such that our network realizes GPS. Based on rigorous theoretical derivations, EGPS and AGPS schemes are respectively proposed according to whether the overall coupling strength is certain or adaptive. Few previous studies have focused on this. It is worth pointing out that both the control input and the adaptive law of the coupling strength in this paper only lie in the information of the crucial node, which implies the significance of the crucial node to some extent. Finally, the effectiveness and feasibility of our theoretical results are verified by two numerical simulation examples.

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Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers

Zhang¹,

Wang²,

Wang³

et al. 2014

Asian Journal of Control

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The objective of this paper is to investigate the synchronization for nonlinear time-delayed coupling complex dynamic networks with different dimensional nodes through the use of decentralized dynamic compensation controllers. We propose a nonlinear time-delayed coupling complex dynamic network model with similar nonlinear nodes, whose dimensions admit differences. For this kind of network model, based on Barbalat's lemma, decentralized dynamic compensation controllers are designed for the state synchronization of the coupled nodes under some mathematical conditions. In addition, the synchronization manifold is defined as an invariant manifold, which is regarded as the generalized case of the networks with the same node dynamics. Finally, numerical examples with chaotic and hyperchaotic nodes are presented to verify the effectiveness of our theoretical results.

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The synchronization of complex dynamical networks with similar nodes and coupling time-delay

Cited by 21 publications

References 24 publications

Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

Synchronization for non-dissipatively coupled time-varying complex dynamical networks with delayed coupling nodes

Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller

Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers

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