publication . Article . Other literature type . Preprint . 2016

weakly coupled oscillators in a slowly varying world

Park, Youngmin; Ermentrout, Bard;
Open Access
  • Published: 05 Mar 2016 Journal: Journal of Computational Neuroscience, volume 40, pages 269-281 (issn: 0929-5313, eissn: 1573-6873, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
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 this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the metho...
Subjects
free text keywords: Sensory Systems, Cognitive Neuroscience, Cellular and Molecular Neuroscience, Theory of computation, Mathematics, Adiabatic theorem, Oscillation, Modulation, Control theory, Perturbation (astronomy), Coupling, Mathematics - Dynamical Systems, Quantitative Biology - Neurons and Cognition
Related Organizations
Funded by
NSF| Interactions between Stimuli and Spatiotemporal Activity
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1219753
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
26 references, page 1 of 2

[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.

[11] Natalia Gorelova, Jeremy K Seamans, and Charles R Yang. Mechanisms of dopamine activation of fast-spiking interneurons that exert inhibition in rat prefrontal cortex. Journal of Neurophysiology, 88(6):3150{3166, 2002.

[12] Boris S Gutkin, G Bard Ermentrout, and Alex D Reyes. Phase-response curves give the responses of neurons to transient inputs. Journal of Neurophysiology, 94(2):1623{1635, 2005.

[13] Ho Young Jeong and Boris Gutkin. Synchrony of neuronal oscillations controlled by GABAergic reversal potentials. Neural Computation, 19(3):706{729, 2007.

[14] James P Keener. Principles of applied mathematics. Addison-Wesley, 1988.

[15] N. Kopell and L.N. Howard. Plane wave solutions to reaction di usion equations. 52:291{328, 1973.

26 references, page 1 of 2
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