The adaptive coupling scheme and the heterogeneity in intrinsic frequency and degree distributions of the complex networks

Ren, Quansheng; He, Mingli; Yu, Xiaoqian; Long, Qiufeng; Zhao, Jianye

doi:10.1016/j.physleta.2013.10.031

Cited by 8 publications

(13 citation statements)

References 43 publications

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“…Adaptive scheme can suppress the negative effect of the heterogeneity in oscillator networks [215][216][217][218]. Even in a system of identical Kuramoto oscillators, the presence of coupling plasticity induces the occurrence of multi-stable states, i.e., the existence of a desynchronized state and a state consisting of two anti-phase clusters [219].…”

Section: Time-varying Couplingmentioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: Time-varying Couplingmentioning

confidence: 99%

“…Other adaptive mechanisms proportional to the instantaneous phase difference between the oscillators have also been considered [216,224,227]. For instance, Aoki and Aoyagi [228] investigated coevolving dynamics in a weighted network of identical oscillators as followṡ…”

Section: Cmentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

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“…In order to analyze the stability of the closed-loop system (25), it is natural to consider the same Lyapunov function defined in (19). In addition, let us consider the same adaptation laws as in (13).…”

Section: Distributed Adaptive Synchronization With Quantized Informationmentioning

confidence: 99%

“…In [18] a set of adaptive strategies for synchronization and consensus of complex networks of dynamical systems is presented. The authors in [19] devise an adaptive scheme to achieve phase synchronization by suppressing the negative effect of the heterogeneity in the network, while in [20] protocols are designed to adaptively interact with system dynamics and preserve the sum of all incoming pairwise coupling strengths. In [21] a co-evolutionary rewiring strategy that depends only on the phase differences of neighboring oscillators is studied for Kuramoto units.…”

Section: Introductionmentioning

confidence: 99%

Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information

Baldi

Tao

Kosmatopoulos

2019

IET Control Theory & Applications

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In this work we study adaptive synchronization in networks with Kuramoto units whose parameters are unknown and where measurements are quantized over the communication network (therefore information is limited). We show that, for an undirected connected graph, synchronization is enabled via appropriate adaptive protocols that counteract the effect of heterogeneity, uncertainty, and quantized information. In particular, to address heterogeneity and uncertainty, appropriate adaptive laws are designed to drive the network to frequency synchronization; to address quantized information, a dynamic quantizer is introduced and embedded into the adaptive mechanism via a zooming-based approach (therefore with hybrid dynamics). The resulting protocol ends up being an adaptive hybrid synchronization strategy that can be distributed throughout the network: the quantizer is co-designed with the controller, as typical for zooming-based quantization. The proposed integrated adaptation+quantization protocol guarantees asymptotic synchronization to a desired frequency, which is shown via an appropriately designed distributed Lyapunov function. Numerical simulations are also used to demonstrate the effectiveness of the proposed protocol.

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“…In [20] a set of adaptive strategies for synchronization and consensus of complex networks of dynamical systems is presented: the main limitation of these approaches is that they address networks composed of identical oscillators. The authors in [21] devise an adaptive scheme to achieve phase synchronization by suppressing the negative effect of the heterogeneity in the network, while in [22] protocols are designed to adaptively interact with system dynamics and preserve the sum of all incoming pairwise coupling strengths. In [23] a co-evolutionary rewiring strategy that depends only on the phase differences of neighboring oscillators is studied for Kuramoto agents.…”

Section: Introductionmentioning

confidence: 99%

Adaptive synchronization in networks with heterogeneous uncertain Kuramoto-like units

Azzollini

Baldi

Kosmatopoulos

2018

2018 European Control Conference (ECC)

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We analyze adaptive synchronization capabilities in networks with Kuramoto-like units whose dynamical features are unknown and thus synchronization protocols must exhibit co-evolution capabilities. In the presence of heterogeneous and uncertain units, synchronization should be enabled by appropriate adaptive protocols that counteract the effect of heterogeneity. An interaction protocol is presented that is used by the units to communicate with each other: the protocol is based on a distributed disagreement measure. The aim of the protocol is to adapt feedback and coupling gains, so as to guarantee the emergence of a synchronous solution. The adaptive strategy is distributed, i.e. each unit self-determines the strength of its gains by using only neighboring measurements. Convergence of the synchronization error to zero is shown via Lyapunov analysis, and numerical examples demonstrate the effectiveness of the proposed protocol.

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The adaptive coupling scheme and the heterogeneity in intrinsic frequency and degree distributions of the complex networks

Cited by 8 publications

References 43 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information

Adaptive synchronization in networks with heterogeneous uncertain Kuramoto-like units

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