Exponential Cluster Phase Synchronization Conditions for Second-order Kuramoto Oscillators

2021 ◽  
pp. 1-1
Author(s):  
Liang Wu ◽  
Haoyong Chen ◽  
Tasarruf Bashir
Keyword(s):  
Phase Synchronization ◽  
Second Order ◽  
Kuramoto Oscillators ◽  
Cluster Phase

Remarks on the complete synchronization for the Kuramoto model with frustrations

2018 ◽  
Vol 16 (04) ◽  
pp. 525-563 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Hwa Kil Kim ◽  
Jinyeong Park
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Prototype Model ◽  
Frequency Synchronization ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Kuramoto Oscillators ◽  
Applicable Range ◽  
The Kuramoto Model ◽  
Complete Frequency

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

scholarly journals Transmission time delays organize the brain network synchronization

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180132 ◽  
Author(s):  
Spase Petkoski ◽  
Viktor K. Jirsa
Keyword(s):  
Time Delays ◽  
Phase Synchronization ◽  
Brain Regions ◽  
Brain Network ◽  
Temporal Organization ◽  
Delay Systems ◽  
Oscillatory Dynamics ◽  
Wide Range ◽  
Kuramoto Oscillators ◽  
The Brain

The timing of activity across brain regions can be described by its phases for oscillatory processes, and is of crucial importance for brain functioning. The structure of the brain constrains its dynamics through the delays due to propagation and the strengths of the white matter tracts. We use self-sustained delay-coupled, non-isochronous, nonlinearly damped and chaotic oscillators to study how spatio-temporal organization of the brain governs phase lags between the coherent activity of its regions. In silico results for the brain network model demonstrate a robust switching from in- to anti-phase synchronization by increasing the frequency, with a consistent lagging of the stronger connected regions. Relative phases are well predicted by an earlier analysis of Kuramoto oscillators, confirming the spatial heterogeneity of time delays as a crucial mechanism in shaping the functional brain architecture. Increased frequency and coupling are also shown to distort the oscillators by decreasing their amplitude, and stronger regions have lower, but more synchronized activity. These results indicate specific features in the phase relationships within the brain that need to hold for a wide range of local oscillatory dynamics, given that the time delays of the connectome are proportional to the lengths of the structural pathways. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals Condensation of Synchronous Orbits on Complex Networks

2021 ◽  
Author(s):  
Ruiwu Niu ◽  
Xiaoqun Wu ◽  
Jianwen Feng ◽  
Gui-jun Pan ◽  
Jun-an Lu ◽  
...  
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Phase Synchronization ◽  
Single Layer ◽  
The Other ◽  
Frequency Synchronization ◽  
Synchronization Process ◽  
Mechanics Analysis ◽  
Kuramoto Oscillators

Abstract In this paper we study frequency synchronization of Kuramoto oscillators. We find a typical phenomenon of condensed synchronous orbits on single-layer or duplex networks through statistical mechanics analysis and numerical simulations, where the distribution of synchronous orbits is in a bell-shaped form. Further, we investigate phase synchronization on single-layer and duplex networks with different distributions of inherent frequencies. We find that normally distributed inherent frequencies with low variances are more beneficial for phase synchronization, and separately distributed inherent frequencies can slow down the synchronization process. In the end, we investigate the influence of one layer's inherent frequencies on the other layer's phase synchronization through inter-layer couplings. Interestingly, we find that one layer's inherent frequencies with a highly condensed distribution can greatly improve phase synchronization on the other layer. The results shed new lights to our understanding of the nature of synchronization on single-layer as well as multilayer complex networks of coupled Kuramoto oscillators.

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