Clustering and phase synchronization in populations of coupled phase oscillators

Cascallares, Guadalupe; Gleiser, Pablo M.

doi:10.1140/epjb/e2015-60314-0

Cited by 6 publications

(4 citation statements)

References 34 publications

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“…Recent work has focussed on describing a theoretical basis for the emergence and stability of such clusters [45][46][47][48][49], suggesting they emerge as a result of strong intra-cluster and weak inter-cluster connections as well as similarity in frequencies of oscillators within each cluster [50]. Much of this work has been theoretical, in small systems, and systems with inherent structure, and we replicate much of the findings here.…”

Section: Discussionsupporting

confidence: 72%

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

2023

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Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.

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Section: Discussionsupporting

confidence: 72%

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

2023

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“…Also, it is involved in vital functions e.g. circadian rhythms [10,11], the functioning of the heart due to the synchronization of pacemaker cells [12,13] and, physiological brain activity [14][15][16]. Conversely, abnormal neural synchronization is linked to neurological disorders like epilepsy or Parkinson's disease [17,18].…”

Section: Introductionmentioning

confidence: 99%

Influence of cumulative damage on synchronization of Kuramoto oscillators on networks

Eraso-Hernandez,

Riascos

2023

J. Phys. A: Math. Theor.

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In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random phases. The process of synchronization is a global function performed by a system that gradually changes when the damage weakens individual connections of the network. We explore diverse structures characterized by different topologies. Among these are deterministic networks as a wheel or the lattice formed by the movements of the knight on a chess board, and random networks generated with the Erd\H{o}s-Rényi and Barab\'asi-Albert algorithms. In addition, we study the synchronization times of 109 non-isomorphic graphs with six nodes. The synchronization times and other introduced quantities are sensitive to the impact of damage, allowing us to measure the reduction of the capacity of synchronization and classify the effect of damage in the systems under study. This approach is general and paves the way for the exploration of the effect of damage accumulation in diverse dynamical processes in complex systems.

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“…After decades of the development, the synchronization forms of complex networks have become more diverse. Apart from global synchronization, 8 robust synchronization 9 in the past, some novel synchronization types, such as generalized synchronization, 10 cluster synchronization, 11 and impulsive synchronization 12 have been discussed in depth.…”

Section: Introductionmentioning

confidence: 99%

Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols

Xuan

Tang

Park

et al. 2021

Adaptive Control & Signal

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This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time-varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster-tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples.

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Clustering and phase synchronization in populations of coupled phase oscillators

Cited by 6 publications

References 34 publications

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

Influence of cumulative damage on synchronization of Kuramoto oscillators on networks

Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols

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