Weakly Coupled Oscillators in a Slowly Varying World

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Park, Youngmin; Ermentrout, Bard;

We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply th... View more
  • References (26)
    26 references, page 1 of 3

    [1] Eric Brown, Je Moehlis, and Philip Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Computation, 16(4):673{715, 2004.

    [2] John R Cressman Jr, Ghanim Ullah, Jokubas Ziburkus, Steven J Schi , and Ernest Barreto. The in uence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 26(2):159{ 170, 2009.

    [3] Per Danzl, Robert Hansen, Guillaume Bonnet, and Je Moehlis. Partial phase synchronization of neural populations due to random Poisson inputs. Journal of Computational Neuroscience, 25(1):141{157, 2008.

    [4] Bard Ermentrout. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students, volume 14. SIAM, 2002.

    [5] Bard Ermentrout, Matthew Pascal, and Boris Gutkin. The e ects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Computation, 13(6):1285{1310, 2001.

    [6] G Bard Ermentrout, Bryce Beverlin II, and Theoden Neto . Phase response curves to measure ion channel e ects on neurons. In Phase response curves in neuroscience, pages 207{236. Springer, 2012.

    [7] G Bard Ermentrout, Roberto F Galan, and Nathaniel N Urban. Reliability, synchrony and noise. Trends in neurosciences, 31(8):428{434, 2008.

    [8] G.Bard Ermentrout. n:m phase-locking of weakly coupled oscillators. Journal of Mathematical Biology, 12(3):327{342, 1981.

    [9] George Bard Ermentrout and Nancy Kopell. Frequency plateaus in a chain of weakly coupled oscillators, I. SIAM Journal on Mathematical Analysis, 15(2):215{237, 1984.

    [10] Roberto F Galan, G Bard Ermentrout, and Nathaniel N Urban. Optimal time scale for spike-time reliability: theory, simulations, and experiments. Journal of Neurophysiology, 99(1):277{283, 2008.

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