Quadratic Approximations for the Isochrons of Oscillators: A General Theory, Advanced Numerical Methods, and Accurate Phase Computations

@article{Suvak2010QuadraticAF,
  title={Quadratic Approximations for the Isochrons of Oscillators: A General Theory, Advanced Numerical Methods, and Accurate Phase Computations},
  author={Onder Suvak and Alper Demir},
  journal={IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems},
  year={2010},
  volume={29},
  pages={1215-1228}
}
The notion of isochrons for oscillators, introduced by Winfree and thereon heavily utilized in mathematical biology, were instrumental in introducing a notion of generalized phase and form the basis for oscillator perturbation analyses. Computing isochrons is a hard problem, existing brute-force methods incurring exponential complexity. In this paper, we present a precise and carefully developed theory and numerical techniques for computing local but quadratic approximations for isochrons… CONTINUE READING
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