Perfect synchronization in networks of phase-frustrated oscillators

Kundu, Prosenjit; Hens, Chittaranjan; Barzel, Baruch; Pal, Pinaki

doi:10.1209/0295-5075/120/40002

Cited by 20 publications

(14 citation statements)

References 43 publications

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“…is the DC bias current. It is to be mentioned that the isolated RSCJ model has similarities with the Sakaguchi-Kuramoto phase model with inertia [43][44][45] and also with the working model of a power grid [46]. In the absence of coupling ( = 0) and a = 1.5, each node can reveal two types of dynamics: oscillatory spiking behavior (I i > 1.0) and a quiescent state (I i < 1.0).…”

Section: Prediction Of Bursting and Clustering: Network Of Josepmentioning

confidence: 99%

Predicting bursting in a complete graph of mixed population through reservoir computing

Saha

Mishra

Ghosh

et al. 2020

Phys. Rev. Research

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We report our investigation and success story, to an extent, on the prediction of spiking and bursting dynamics in globally coupled networks, using echo state network/reservoir computing-based learning procedure. Two exemplary dynamical models, Josephson junctions and Hindmarsh-Rose neurons, are used to construct two separate networks and thereby illustrate the efficacy of our strategy. In the absence of coupling, the networks consist of mixed populations in which few nodes are oscillatory (self-sustained spiking) and the rest of the nodes maintain a quiescent state. When single-input data from one oscillatory node of a network (under stronger interactions between the nodes) is used for learning, the ESN is able to predict the key dynamical features (spiking and bursting) of the other nodes. In comparison, the machine performs with improved predictions if it is fed with two inputs: one from the oscillatory population and another from an excitable population. The machine's leaking parameter plays a crucial role, which can be tuned appropriately to enhance prediction. Furthermore, a cluster synchronization in the mixed population is confirmed from the machine-generated output signals. Our work is expected to be useful as a burst predictor.

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Section: Prediction Of Bursting and Clustering: Network Of Josepmentioning

confidence: 99%

Predicting bursting in a complete graph of mixed population through reservoir computing

Saha

Mishra

Ghosh

et al. 2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, the Kuramoto model as a paradigm for general oscillator models has been intensively investigated recently [7], from the perspective of networked control [10], selforganized synchronization [12][13][14][15][16][17], to stability against even large perturbations [18,19]. e further investigation of the Kuramoto model with or without inertia attracts great interest from the aspects of, e.g., the optimal placement of virtual inertia for system performance [20] and for perfect synchronization [21,22], non-Gaussian frequency fluctuations described by Levy-stable laws [23]. From the viewpoint of power grid operators, it is vital yet challenging to enhance network stability in complex power grids, especially in the presence of electricity markets [4].…”

Section: Introductionmentioning

confidence: 99%

How Price-Based Frequency Regulation Impacts Stability in Power Grids: A Complex Network Perspective

Zhu

Lü

et al. 2020

Complexity

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With the deregulation of modern power grids, electricity markets are playing a more and more important role in power grid operation and control. However, it is still questionable how the real-time electricity price-based operation affects power grid stability. From a complex network perspective, here we investigate the dynamical interactions between price-based frequency regulations and physical networks, which results in an interesting finding that a local minimum of network stability occurs when the response strength of generators/consumers to the varying price increases. A case study of the real world-based China Southern Power Grid demonstrates the finding and exhibits a feasible approach to network stability enhancement in smart grids. This also provides guidance for potential upgrade and expansion of the current power grids in a cleaner and safer way.

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“…In [33], it was observed that lags alone may be used to control the system to a predefined frequency for the complete network case. In [34], a similar mechanism was used for sparser graphs to enable frequencies to be selected in order to provide for perfect synchronisation. In our previous paper [35] we showed how a form of codynamics, namely adaptive lags, where the λ i become functions of time with their own evolution equation, can improve synchronisation for sparse networks -indeed, achieve perfect phase synchronisation.…”

Section: Introductionmentioning

confidence: 99%

Controlling and enhancing synchronization through adaptive phase lags

Kalloniatis

Brede

2019

Phys. Rev. E

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We compare two methods for controlling synchronisation in the Kuramoto model on an undirected network. The first is by driving selected oscillators at a desired frequency by coupling to an external driver, and the second is by including adaptive lags-or dynamical frustrations-within the Kuramoto interactions, with the lags evolving according to a dynamics as a function of the reference frequency with an associated time-constant. Performing numerical simulations with random regular graphs, we find that above a certain connectivity driving via adaptive lags allows for stronger alignment to the external frequency at lower value of the time-constant compared to the corresponding coupling strength for the externally driven model. Numerical results are backed up by equilibrium analysis based on a fixed point ansatz for frequency synchronised clusters where we solve the spectrum of the associated Jacobian matrix. We find that at low connectivity the external driving mechanism is successful down to lower densities of controlled oscillators where the adaptive lag approach is Lyapunov unstable at all densities. As connectivity increases, however, the adaptive lag mechanism shows stability over similar ranges of density to the external driving and proves superior in terms of tighter splays of oscillators. In particular, the threshold for instability for the adaptive lag model shows robustness against variations in the associated time constant down to lower densities of controlled oscillators. A simple intuitive model emerges based on the interaction between splayed clusters close to a critical point.

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Perfect synchronization in networks of phase-frustrated oscillators

Cited by 20 publications

References 43 publications

Predicting bursting in a complete graph of mixed population through reservoir computing

Predicting bursting in a complete graph of mixed population through reservoir computing

How Price-Based Frequency Regulation Impacts Stability in Power Grids: A Complex Network Perspective

Controlling and enhancing synchronization through adaptive phase lags

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