Synchronization Of Coupled Oscillators Research Articles

Pinning Synchronization of Coupled Oscillators with Paired Topologies

Pinning Synchronization of Coupled Oscillators with Paired Topologies

A Stochastic Approach to the Synchronization of Coupled Oscillators

This paper deals with an optimal control problem associated to the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation.

Global Phase and Magnitude Synchronization of Coupled Oscillators With Application to the Control of Grid-Forming Power Inverters

In this paper, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model, we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback based on relative state information and local measurements that induces consensus-like dynamics. We show that, under a mild stability condition, the combination of the synchronizing feedback with a decentralized magnitude control law renders the oscillators’ almost globally asymptotically stable with respect to set points for the phase shift, frequency, and magnitude. We apply these result to rigorously solve an open problem in control of inverter-based ac power systems. In this context, the proposed control strategy can be implemented using purely local information, induces a grid-forming behavior, and ensures that a network of ac power inverters is almost globally asymptotically stable with respect to a prespecified solution of the ac power-flow equations. Moreover, we show that the controller exhibits a droop-like behavior around the standard operating point, thus, making it backward compatible with the existing power system operation.

A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter

This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed “chimeric synchronization”. The family of metrics is proposed to create a neural network information converter based on a network of pulsed oscillators. In addition to transforming input information from digital to analogue, the converter can perform information processing after training the network by selecting control parameters. In the proposed neural network scheme, the data arrives at the input layer in the form of current levels of the oscillators and is converted into a set of non-repeating states of the chimeric synchronization of the output oscillator. By modelling a thermally coupled VO2-oscillator circuit, the network setup is demonstrated through the selection of coupling strength, power supply levels, and the synchronization efficiency parameter. The distribution of solutions depending on the operating mode of the oscillators, sub-threshold mode, or generation mode are revealed. Technological approaches for the implementation of a neural network information converter are proposed, and examples of its application for image filtering are demonstrated. The proposed method helps to significantly expand the capabilities of neuromorphic and logical devices based on synchronization effects.

Synchronization of Coupled Oscillators on a Two-Dimensional Plane.

The effect of the transfer rate of signal molecules on coupled chemical oscillators arranged on a two-dimensional plane was systematically investigated in this paper. A microreactor equipped with a surface acoustic wave (SAW) mixer was applied to adjust the transfer rate of the signal molecules in the microreactor. The SAW mixer with adjustable input powers provided a simple means to generate different mixing rates in the microreactor. A robust synchronization of the oscillators was found at an input radio frequency power of 20 dBm, with which the chemical waves were initiated at a fixed site of the oscillator system. With increasing input power, the frequency of the chemical waves was increased, which agreed well with the prediction given by the time-delayed phase oscillator model. Results from the finite element simulation agreed well with the experimental results.

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.

Synchronization of Coupled Discrete-Time Harmonic Oscillators With Rational Frequency

This technical note studies the synchronization of coupled discrete-time harmonic oscillators with rational frequency under switching topology. The remarkable feature of this problem is that the conditions that merely involve the connectivity structure of topology does not suffice for synchronizing the oscillators. We propose a frequency dependent topology condition that indicates in what way the topology switches, and introduce firmly nonexpansive mapping (FNM) from functional analysis. Under the condition, the synchronization of coupled oscillators is related to an infinite product of FNMs, which share only one zero common fixed point. By a convergence result on infinite product of a finite number of FNM, we present a synchronization result for the coupled oscillators. Finally, a simulation example is given to illustrate the effectiveness of the result.

Synchronization of Coupled Oscillators is a Game

The purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents. Applications are found in neuroscience, biology, and economics, as well as traditional engineering applications. The focus of analysis is a variation of the large population linear quadratic Gaussian (LQG) model of Huang et al. 2007, comprised here of a controlled N-dimensional stochastic differential equation model, coupled only through a cost function. The states are interpreted as phase angles for a collection of heterogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto. A deterministic PDE model is proposed, which is shown to approximate the stochastic system as the population size approaches infinity. Key to the analysis of the PDE model is the existence of a particular Nash equilibrium in which the agents opt out' of the game, setting their controls to zero, resulting in the incoherence' equilibrium. Methods from dynamical systems theory are used in a bifurcation analysis, based on a linearization of the partial differential equation (PDE) model about the incoherence equilibrium. A critical value of the control cost parameter is identified: above this value, the oscillators are incoherent; and below this value (when control is sufficiently cheap) the oscillators synchronize. These conclusions are illustrated with results from numerical experiments.

Resonance Assisted Synchronization of Coupled Oscillators: Frequency Locking without Phase Locking

Frequency locking without phase locking of two coupled nonlinear oscillators is experimentally demonstrated. This synchronization regime is found for two coupled laser modes, beyond the phase-locking range fixed by Adler's equation, because of a resonance mechanism. Specifically, we show that the amplitudes of the two modes exhibit strong fluctuations that produce average frequency synchronization, even if the instantaneous phases are unlocked. The experimental results are in good agreement with a theoretical model.

Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Duffing oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.

Synchronization of Coupled Oscillators on Newman–WattsSmall-World Networks

We investigate the collection behaviour of coupled phase oscillatorson Newman–Watts small-world networks in one and two dimensions.Each component of the network is assumed as an oscillator andeach interacts with the others following the Kuramoto model. Wethen study the onset of global synchronization of phases andfrequencies based on dynamic simulations and finite-size scaling.Both the phase and frequency synchronization are observed toemerge in the presence of a tiny fraction of shortcuts andenhanced with the increases of nearest neighbours and latticedimensions.

Phase Synchronization in Coupled Oscillators: DynamicalManifestations

Phase synchronized entrainment of coupled oscillators with distributednatural frequencies is studied by exploring the dynamical manifestation.The route from partial to complete phase synchronization is identifiedas a cascade of transitions from high- to low-dimensional tori(quasiperiodicities) interrupted by intermittent chaos. Torus ON-OFFintermittency is found at the onset of desynchronization.Desynchronization-induced chaos originates from the mixing of intermittentON-OFF timescales.

Phase Slips and Phase Synchronization of Coupled Oscillators

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the phase-locking state, simultaneous phase slips of all oscillators and quantized phase shifts in these phase slips are observed. By increasing the coupling, a bifurcation tree from high-dimensional quasiperiodicity to chaos to quasiperiodicity and periodicity is found. Different orders of phase synchronizations of chaotic oscillators and chaotic clusters play the key role for constructing this tree structure.