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On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
, 2005
"... We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using ..."
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Cited by 72 (9 self)
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We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences 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 6 (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.
Conditions for synchronizability in arrays of coupled linear systems
 IEEE Transactions on Automatic Control
"... Synchronization control in arrays of identical outputcoupled continuoustime linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable systems that are detectable form their outputs, a linear feedbac ..."
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Cited by 3 (1 self)
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Synchronization control in arrays of identical outputcoupled continuoustime linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable systems that are detectable form their outputs, a linear feedback law exists under which any number of coupled systems synchronize provided that the (directed, weighted) graph describing the interconnection is fixed and connected. An algorithm generating one such feedback law is presented. It is also shown that for critically unstable systems detectability is not sufficient, whereas fullstate coupling is, for the existence of a linear feedback law that is synchronizing for all connected coupling configurations. 1
LQRbased coupling gain for synchronization of linear systems
 2008. [Online]. Available: http://arxiv.org/pdf/0801.3390
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, 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.
1997 IEEE INTERNATIONAL FREQUENCY CONTROL SYMPOSIUM SPONTANEOUS SYNCHRONIZATION IN NATURE
"... Mutual synchronization of oscillators is ubiquitous in ..."
c © World Scientific Publishing Company TOOLS FOR NETWORK DYNAMICS*
, 2003
"... Networks have been studied mainly by statistical methods which emphasize their topological structure. Here, one collects some mathematical tools and results which might be useful to study both the dynamics of agents living on the network and the networks themselves as evolving dynamical systems. The ..."
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Networks have been studied mainly by statistical methods which emphasize their topological structure. Here, one collects some mathematical tools and results which might be useful to study both the dynamics of agents living on the network and the networks themselves as evolving dynamical systems. They include decomposition of differential dynamics, ergodic techniques, estimates of invariant measures, construction of non deterministic automata, logical approaches,