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On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
 In Proceedings of the American Control Conference
, 2004
"... We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral gra ..."
Abstract

Cited by 58 (8 self)
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We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.
Synchrony and mutual stimulation of yeast cells during fast glycolytic oscillations
, 1992
"... Cell synchrony was investigated during glycolytic oscillations in starved yeast cell suspensions at cell densities ranging from 2 x 1065 x lo7 cells mll. Oscillations in NAD(P)H were triggered by inhibition of mitochondria1 respiration when intracellular NAD(P)H had reached a steady state after gl ..."
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Cited by 4 (0 self)
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Cell synchrony was investigated during glycolytic oscillations in starved yeast cell suspensions at cell densities ranging from 2 x 1065 x lo7 cells mll. Oscillations in NAD(P)H were triggered by inhibition of mitochondria1 respiration when intracellular NAD(P)H had reached a steady state after glucose addition. Before macroscopic damping of the oscillations, individual yeast cells oscillated in phase with the cell population. After oscillations had damped out macroscopically, a significant fraction of the cells still exhibited oscillatory dynamics, slightly outofphase. At cell concentrations higher than lo7 cells mll the dependence upon celldensity of (i) the damping of glycolytic oscillations and (ii) the amplitude per cell suggested that celltocell interaction occurred. Most importantly, at cell densities exceeding lo7 cells mll the damping was much weaker. A combination of modelling studies and experimental analysis of the kinetics of damping of oscillations and their amplitude, with and without added ethanol, pyruvate or acetaldehyde, suggested that the autonomous glycolytic oscillations of the yeast cells depend upon the balance between oxidative and reductive (ethanol catabolism) fluxes of NADH, which is affected by the extracellular concentration of ethanol. Based on the facts that cell (i) excrete ethanol, (ii) are able to catabolize external ethanol, and (iii) that this catabolism affects their tendency to oscillate, we suggest that the dependence of the oscillations on cell density is mediated through the concentration of ethanol in the medium.
AND
, 909
"... A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finitesize systems may have many different synchr ..."
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A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finitesize systems may have many different synchronized stable solutions which are characterised by different values of the winding number. The lower bound for the critical coupling kc is given, as well as an algorithm for its exact calculation. It is shown that in general phaselocking does not lead to phase coherence in 1D. PACS numbers: 05.45.Xt 1.