Phase dynamics of coupled oscillators reconstructed from data.

@article{Kralemann2008PhaseDO,
  title={Phase dynamics of coupled oscillators reconstructed from data.},
  author={Bj{\"o}rn Kralemann and Laura Cimponeriu and Michael Rosenblum and Arkady Pikovsky and Ralf Mrowka},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={77 6 Pt 2},
  pages={
          066205
        }
}
We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of… 
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stat.physik.uni-potsdam.de
177 Citations
Highly Influential Citations
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Background Citations
49
Methods Citations
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177 Citations

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References

SHOWING 1-10 OF 36 REFERENCES

Uncovering interaction of coupled oscillators from data.

A technique for reconstructing the phase dynamics equations for weakly coupled oscillators from data is developed and it is demonstrated that natural frequencies of oscillators can be recovered if several observations of coupled systems at different coupling strengths are available.

Inferring phase equations from multivariate time series.

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important…

Determination of a coupling function in multicoupled oscillators.

A new method to determine a coupling function in a phase model is theoretically derived for coupled self-sustained oscillators and applied to Belousov-Zhabotinsky (BZ) oscillators. The synchronous…

Predicting mutual entrainment of oscillators with experiment-based phase models.

The experiment-based model properly describes in-phase and antiphase mutual entrainment with positive and negative interactions in small sets as well as dynamical clustering in populations of oscillators.

Inferring Asymmetric Relations between Interacting Neuronal Oscillators

A pilot study in one healthy subject reveals that asymmetry of interactions between different brain areas may strongly change with the transition from external to internal pacing, while the degree of synchronization hardly changes.

Estimation of delay in coupling from time series.

It is demonstrated that a time delay in weak coupling between two self-sustained oscillators can be estimated from the observed time series data and analytically and numerically that irregularity of the phase dynamics is essential for determination of the delay.

Estimation of coupling between time-delay systems from time series.

The method allows one to detect the presence of certain types of linear coupling between two time- delay systems, to define the type, strength, and direction of coupling, and to recover the model equations of coupled time-delay systems from chaotic time series corrupted by noise.

Synchronization - A Universal Concept in Nonlinear Sciences

This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.

Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function

Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling.

A simple method is presented for estimating the phase-resetting curve of real neurons to simplify the complex dynamics of a single neuron to a phase model and illustrate how to infer the existence of coherent network activity from the estimated PRC.