Charge-balanced spike timing control for phase models of spiking neurons

Per Danzl; Ali Nabi; Jeff Moehlis

doi:10.3934/dcds.2010.28.1413

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2010, Volume 28, Issue 4: 1413-1435. Doi: 10.3934/dcds.2010.28.1413

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Charge-balanced spike timing control for phase models of spiking neurons

1.
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

Received: September 30, 2009

Revised: January 31, 2010

Published: November 2010

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Abstract

This paper explores event-based feedback schemes for controlling spike timing in phase models of neurons with the constraint of a charge-balanced stimulus over a period of stimulation. We present an energy-optimal control system based on variational methods. We also present a biologically-inspired quasi-impulsive control system that, mimicking the signaling behavior of real neurons, can achieve reference phase tracking. Applied to a pacemaker-driven ensemble, this control can achieve desynchronization using a set of charge-balanced stimuli.

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Mathematics Subject Classification: Primary: 92C20, 93C15; Secondary: 37N25.

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