scholarly journals Modeling Frequency Reduction in Human Groups Performing a Joint Oscillatory Task

2022 ◽  
Vol 12 ◽  
Author(s):  
Carmela Calabrese ◽  
Benoît G. Bardy ◽  
Pietro De Lellis ◽  
Mario di Bernardo
Keyword(s):  
Experimental Observation ◽  
Kuramoto Model ◽  
Biologically Relevant ◽  
Kuramoto Oscillators ◽  
Multi Agent ◽  
Group Synchronization

In human groups performing oscillatory tasks, it has been observed that the frequency of participants' oscillations reduces when compared to that acquired in solo. This experimental observation is not captured by the standard Kuramoto oscillators, often employed to model human synchronization. In this work, we aim at capturing this observed phenomenon by proposing three alternative modifications of the standard Kuramoto model that are based on three different biologically-relevant hypotheses underlying group synchronization. The three models are tuned, validated and compared against experiments on a group synchronization task, which is a multi-agent extension of the so-called mirror game.

Static group synchronization of second-order multi-agent systems via pinning control

2019 ◽  
Vol 356 (9) ◽  
pp. 4842-4858 ◽  
Author(s):  
Xiang-Gui Guo ◽  
Hong-Jian Li ◽  
Jun-Jie Zhao ◽  
Wei-Wei Che
Keyword(s):  
Pinning Control ◽  
Second Order ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Group Synchronization ◽  
Static Group

Consensus stability in multi-agent systems with periodically switched communication topology using Floquet theory

2020 ◽  
pp. 014233122096905
Author(s):  
Mohammad Maadani ◽  
Eric A Butcher
Keyword(s):  
Feedback Linearization ◽  
Floquet Theory ◽  
Kuramoto Model ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Unstable Subsystems ◽  
Special Cases ◽  
Communication Topology ◽  
Multi Agent ◽  
The Stability

The stability of consensus in linear and nonlinear multi-agent systems with periodically switched communication topology is studied using Floquet theory. The proposed strategy is illustrated for the cases of consensus in linear single-integrator, higher-order integrator, and leader-follower consensus. In addition, the application of Floquet theory in analyzing special cases such as switched systems with joint connectivity, unstable subsystems, and nonlinear systems, including the use of feedback linearization and local linearization in the Kuramoto model, is also studied. By utilizing Floquet theory for multi-agent systems with periodically switched communication topologies, one can simultaneously evaluate the effects of each subsystem’s convergence rate and dwell time on overall behavior. Numerical simulation results are presented to demonstrate the efficacy of the proposed approach in stability analysis of all these cases.

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 THE KURAMOTO MODEL SUBJECT TO A FLUCTUATING ENVIRONMENT: APPLICATION TO BRAINWAVE DYNAMICS

2012 ◽  
Vol 11 (01) ◽  
pp. 1240011 ◽  
Author(s):  
A. C. HALE ◽  
T. HANSARD ◽  
L. W. SHEPPARD ◽  
P. V. E. McCLINTOCK ◽  
A. STEFANOVSKA
Keyword(s):  
Quantitative Measure ◽  
Kuramoto Model ◽  
Living Systems ◽  
Phase Dynamics ◽  
Fluctuating Environment ◽  
Kuramoto Oscillators ◽  
The Kuramoto Model ◽  
Model Subject

We consider the phase dynamics of an ensemble of Kuramoto oscillators whose eigenfrequencies are perturbed to model the openness of living systems, and we show that it exhibits time-localized epochs of synchrony. A new quantitative measure is used to show that the model compares well with electroencephalography data recorded from a healthy awake human.

scholarly journals An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-Bénard Convection

2019 ◽  
Author(s):  
Atanu Chatterjee ◽  
Nicholas Mears ◽  
Yash Yadati ◽  
Germano Iannacchione
Keyword(s):  
Soft Matter ◽  
Kuramoto Model ◽  
Square Lattice ◽  
General Nature ◽  
Driven Systems ◽  
Emergent Order ◽  
Kuramoto Oscillators ◽  
Far From Equilibrium ◽  
Spatio Temporal ◽  
The Kuramoto Model

Soft-matter systems when driven out-of-equilibrium often give rise to structures that usually lie in-between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayeligh-Bénard convection system which when driven out-of-equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-assemble are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to look for connections between among these systems and systems in general which give rise to emergent order when driven out-of-equilibrium.

scholarly journals An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 561 ◽  
Author(s):  
Atanu Chatterjee ◽  
Nicholas Mears ◽  
Yash Yadati ◽  
Germano S. Iannacchione
Keyword(s):  
Soft Matter ◽  
Kuramoto Model ◽  
Square Lattice ◽  
General Nature ◽  
Emergent Order ◽  
Bénard Convection ◽  
Benard Convection ◽  
Kuramoto Oscillators ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh–Bénard convection system which when driven out of equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out of equilibrium. This study, thus acts as a foundation for modeling a complex system as a two-state system, where the states: order and disorder can coexist as the system is driven away from equilibrium.

scholarly journals Collective almost synchronization-based model to extract and predict features of EEG signals

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Phuong Thi Mai Nguyen ◽  
Yoshikatsu Hayashi ◽  
Murilo Da Silva Baptista ◽  
Toshiyuki Kondo
Keyword(s):  
Dynamic Regime ◽  
Kuramoto Model ◽  
Eeg Signals ◽  
Forecasting Error ◽  
Proposed Model ◽  
Eeg Data ◽  
Kuramoto Oscillators ◽  
Outstanding Result ◽  
The Brain ◽  
Computing Models

Abstract Understanding the brain is important in the fields of science, medicine, and engineering. A promising approach to better understand the brain is through computing models. These models were adjusted to reproduce data collected from the brain. One of the most commonly used types of data in neuroscience comes from electroencephalography (EEG), which records the tiny voltages generated when neurons in the brain are activated. In this study, we propose a model based on complex networks of weakly connected dynamical systems (Hindmarsh–Rose neurons or Kuramoto oscillators), set to operate in a dynamic regime recognized as Collective Almost Synchronization (CAS). Our model not only successfully reproduces EEG data from both healthy and epileptic EEG signals, but it also predicts EEG features, the Hurst exponent, and the power spectrum. The proposed model is able to forecast EEG signals 5.76 s in the future. The average forecasting error was 9.22%. The random Kuramoto model produced the outstanding result for forecasting seizure EEG with an error of 11.21%.

scholarly journals Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays

2018 ◽  
Vol 28 (05) ◽  
pp. 1830014 ◽  
Author(s):  
Per Sebastian Skardal
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Critical Time ◽  
General System ◽  
Stability Diagram ◽  
Coupled Systems ◽  
Kuramoto Model ◽  
Codimension Two ◽  
Heterogeneous Interaction ◽  
Kuramoto Oscillators

We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the bifurcations in the system. Of particular interest is the onset of hysteresis where both the incoherent and partially synchronized states are stable for a range of coupling strengths — this occurs at a codimension-two point at the intersection between a Hopf bifurcation and saddle node bifurcation of cycles. By studying this codimension-two point we find the full set of characteristic time delays and natural frequencies where bistability exists and identify the critical time delay and critical natural frequency below which bistability does not exist. Finally, we examine the dynamics of the more general system where time delays are drawn from a Gamma distribution, finding that more homogeneous time delay distributions tend to both promote the onset of synchronization and inhibit the presence of hysteresis.

Probing to Observe Neural Dynamics Investigated with Networked Kuramoto Oscillators

2016 ◽  
Vol 27 (01) ◽  
pp. 1650038 ◽  
Author(s):  
Elma O’Sullivan-Greene ◽  
Levin Kuhlmann ◽  
Ewan S. Nurse ◽  
Dean R. Freestone ◽  
David B. Grayden ◽  
...  
Keyword(s):  
Relative Size ◽  
Kuramoto Model ◽  
Brain Dynamics ◽  
Neural Engineering ◽  
Seizure Prediction ◽  
Active Probing ◽  
Kuramoto Oscillators ◽  
Non Gaussian ◽  
Passive Measurements

The expansion of frontiers in neural engineering is dependent on the ability to track, detect and predict dynamics in neural tissue. Recent innovations to elucidate information from electrical recordings of brain dynamics, such as epileptic seizure prediction, have involved switching to an active probing paradigm using electrically evoked recordings rather than traditional passive measurements. This paper positions the advantage of probing in terms of information extraction, by using a coupled oscillator Kuramoto model to represent brain dynamics. While active probing performs better at observing underlying system synchrony in Kuramoto networks, especially in non-Gaussian measurement environments, the benefits diminish with increasing relative size of electrode spatial resolution compared to synchrony area. This suggests probing will be useful for improved characterization of synchrony for suitably dense electrode recordings.

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