Robustness of network coherence in asymmetric unicyclic graphs

Chen, Jing; Jing, Ting; Sun, Weigang

doi:10.1142/s021797922150301x

Cited by 6 publications

(5 citation statements)

References 22 publications

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“…Compared to numerical results on the coherence, exact expressions facilitates the interplay between the coherence and network topology. For this purpose, we propose a family of ring-trees networks [24] as our models and we set different forms of hub nodes and leaders. The ring network is formed by a circle of order n. The structural asymmetry of networks is adjusted by the number of hubs.…”

Section: Asymmetric Networkmentioning

confidence: 99%

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Topology design for leader-follower coherence in noisy asymmetric networks

Chen¹,

Sun²,

Wang³

2022

Phys. Scr.

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In this paper, we aim to study the effect of the leader's positions in leader-follower coherence quantified by the spectrum in noisy asymmetric networks with a set of hub nodes. In order to compare the impact of leader selection in different ways on the studied coherence, we choose a family of ring-trees networks to conveniently assign the leaders and hubs. Based on the regular network topology and matrix theories, we obtain analytical solutions for the leader-follower coherence regarding network parameters and the number of leaders. Using these expressions, we then obtain exact relations among the coherences and show that the leader's positions and network parameters have a profound impact on the coherence. More specifically, the network with one hub displays better coherence than the networks with two hubs. In addition, two adjacent and nonadjacent hubs lead to distinct performance of leader-follower consensus dynamics that depends on network parameters and assigned leaders in the ring or the tree network.

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Section: Asymmetric Networkmentioning

confidence: 99%

“…Based on results from [24], we have the coefficients of constant term and first-order term of λ in equation (6), that is,…”

Section: Exact Calculations Of Leader-follower Coherencementioning

confidence: 99%

Topology design for leader-follower coherence in noisy asymmetric networks

Chen¹,

Sun²,

Wang³

2022

Phys. Scr.

Self Cite

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“…Subsequently, additional studies have delved into the analysis of network coherence in deterministic networks. These studies have explored aspects such as introducing weighted factors, scale-free loop structures, multi-layer networks, asymmetric networks, and optimization techniques [10][11][12][13][14][15][16] and many references cited therein. Furthermore, the calculation of network coherence can be achieved through the global mean first passage time of a random walk [17,18].…”

Section: Introductionmentioning

confidence: 99%

Consensus analysis of chain star networks coupled by leaf nodes

Chen,

Zhou,

Sun

2023

Phys. Scr.

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Coupled star networks coupled by hub nodes have attracted signiﬁcant interest due to the interplay between their coupling forms and dynamics. This paper introduces a novel family of chain star networks that are connected via a small number of leaf nodes. The coherence of these star networks is quantiﬁed using the Laplacian spectrum. By leveraging the network structures, we calculate the characteristic polynomial of the Laplacian matrix and obtain an exact solution for network coherence in relation to network parameters. In addition, we explore the robustness of network coherence against variations in network parameters. Furthermore, we compare the coherence performance of coupled star networks across diﬀerent coupling forms. Our ﬁndings demonstrate that the networks coupled by leaf nodes exhibit better coherence.

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“…Ref. [24] studied the robustness of network coherence and found that asymmetric networks show higher coherence than symmetric networks. The above literature has mainly studied the impact of control protocol design and topology on network consensus but has not considered the impact of different layer connection methods on network consensus.…”

Section: Introductionmentioning

confidence: 99%

Robustness of Consensus of Two-Layer Ring Networks

Gao²,

Shang

et al. 2023

Symmetry

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The topology structure of multi-layer networks is highly correlated with the robustness of consensus. This paper investigates the influence of different interlayer edge connection patterns on the consensus of the two-layer ring networks. Two types of two-layer ring network models are first considered: one is a kind of two-layer ring network with two linked edges between layers (Networks-a), and the other is a kind of two-layer ring network with three linked edges between layers (Networks-b). Using the Laplacian spectrum, the consensus of the network model is derived. The simulation experiments are used to demonstrate the influence of different interlayer edge connection patterns on the consensus of networks. To determine the best edge connection pattern for Networks-a and Networks-b, the number of nodes in a single-layer ring network is denoted by n. The best edge connection pattern for Networks-a is 1 & [(n+2)/2]. Furthermore, n is subdivided into 3k,3k+1,3k+2, and the best edge connection patterns of Networks-b are near 1 & k+1 & 2k+1.

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Robustness of network coherence in asymmetric unicyclic graphs

Cited by 6 publications

References 22 publications

Topology design for leader-follower coherence in noisy asymmetric networks

Topology design for leader-follower coherence in noisy asymmetric networks

Consensus analysis of chain star networks coupled by leaf nodes

Robustness of Consensus of Two-Layer Ring Networks

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