Linearization error in synchronization of Kuramoto oscillators

Ghorban, Samira Hossein; Baharifard, Fatemeh; Hesaam, Bardyaa; Zarei, Mina; Sarbazi-Azad, Hamid

doi:10.1016/j.amc.2021.126464

Cited by 2 publications

(5 citation statements)

References 42 publications

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“…which means that if ω is decomposed with respect to an explicit difference vector θ * , then the eigenvector v 1 has no essential role in Lb(ω). It was already shown (lemma 1 in [27]) that none of eigenvectors v 2 , . .…”

Section: Linear Approximation For Kuramoto Coupled Oscillatorsmentioning

confidence: 92%

“…Let R(t) = (r ω,θ 0 ,κA,H (t)) 2 . In [27], it is shown that if θ satisfies the system ω, θ 0 , κA, H , then…”

Section: Linear Approximation For Kuramoto Coupled Oscillatorsmentioning

confidence: 99%

“…The impact of changes for average and standard deviation of frequency vectors on the order parameter is examined in [27]. Since the average of ω i 's has no impact on the order parameter, without loss of generality, the average of frequency vector ω is assumed to be zero; so ω = σ(ω) and…”

Section: Proof Suppose Thatmentioning

confidence: 99%

“…• Skardal et al in [19] address two classes of optimization problems. In the second class 3 , they propose a function called the synchrony alignment function, denoted by SAF, based on the relation between eigenvectors of Laplacian matrices for networks and intrinsic frequencies of oscillators, in a way that in the linearized regime [27], the lower values of SAF leads to higher amounts of the degree of synchronization in the coupled network. Based on SAF, they developed a rewiring mechanism and experimentally examine that this method significantly increases the degree of synchronization for networks with large coupling strengths, while this is not the case for coupled networks with low coupling strengths.…”

Section: Introductionmentioning

confidence: 99%

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A rewiring mechanism to improve synchronization in Kuramoto networks

Ghorban¹,

Hesaam²,

Sarbazi-Azad³

2022

J. Stat. Mech.

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The emergence of synchronization among a set of individual oscillators that are coupled in a network is an amazing physical phenomenon that appears in many different systems, from natural sciences to even human behavior. The phenomenon has attracted the attention of many researchers in many fields of science and engineering by the science behind its unique collective behavior without some kind of external organization. One of the most popular models for the dynamical evolution of coupled phase oscillators is the Kuramoto model, which gives a simple yet powerful formalization together with a numerical measure called the degree of synchronization. The crucial role of structural properties of the network on the degree of synchronization is analyzed in many researches. One of streamlines, well-known as ‘rewiring’, is to re-design the network structure via rearranging its links to increase or decrease the degree of synchronization. In this study, we propose a rewiring mechanism to improve the degree of synchronization for the coupled heterogeneous oscillators based on global and local information of networks. In our mechanism, the share of each link in the maximum eigenvalue of the Laplacian matrix of the network is considered as local information, together with a global criteria which is defined based on frequencies and eigenvectors of the Laplacian matrix. Experimental results show that the proposed mechanism can improve the order parameter in a more stable manner.

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Section: Linear Approximation For Kuramoto Coupled Oscillatorsmentioning

confidence: 92%

“…Let R(t) = (r ω,θ 0 ,κA,H (t)) 2 . In [27], it is shown that if θ satisfies the system ω, θ 0 , κA, H , then…”

Section: Linear Approximation For Kuramoto Coupled Oscillatorsmentioning

confidence: 99%

Section: Proof Suppose Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A rewiring mechanism to improve synchronization in Kuramoto networks

Ghorban¹,

Hesaam²,

Sarbazi-Azad³

2022

J. Stat. Mech.

Self Cite

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show abstract

“…Considering that many industry applications simply need the transient or finite working time, such as electronic circuit, chemical reaction process, and flight control, in which the constrained state variables are required to avoid exceeding the specified physical threshold over certain time interval. Therefore, finite time synchronization (FTS) has been attracted increasing attention and many classical results have been obtained accordingly Luo and Yao (2019); Chen et al (2020b); Cui et al (2020); Cai and Huang (2018); Chen et al (2019); Muhammadhaji et al (2017); Wu et al (2019); Shg et al (2021). Finite time synchronization of MNNs have been achieved by using 1-norm Lyapunov functionals and algebra analytical approach in Yang and Ho (2015).…”

Section: Introductionmentioning

confidence: 99%

New criteria for predefined finite time synchronization of memristor-based neural networks

Lin

2022

Journal of Vibration and Control

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The fast synchronization problem of memristor-based neural networks is studied in this article. Firstly, a novel predefined finite time stability of a class of nonlinear dynamical systems is investigated under the incomplete beta function, complete beta function, and inequality technology. Then, an active predefined finite time controller is designed that guarantees finite time stability of synchronization errors of two memristor-based neural networks with/without proportional delay. Some simulation results are presented to show the effectiveness of theoretical results.

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Linearization error in synchronization of Kuramoto oscillators

Cited by 2 publications

References 42 publications

A rewiring mechanism to improve synchronization in Kuramoto networks

A rewiring mechanism to improve synchronization in Kuramoto networks

New criteria for predefined finite time synchronization of memristor-based neural networks

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