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December  2010, 28(4): 1413-1435. doi: 10.3934/dcds.2010.28.1413

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

Per Danzl 1, , Ali Nabi 1, and  Jeff Moehlis 1,

1. 

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, United States, United States, United States

Received  October 2009 Revised  February 2010 Published  June 2010

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.
Keywords: control, Mathematical neuroscience, phase models..
Mathematics Subject Classification: Primary: 92C20, 93C15; Secondary: 37N2.
Citation: Per Danzl, Ali Nabi, Jeff Moehlis. Charge-balanced spike timing control for phase models of spiking neurons. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1413-1435. doi: 10.3934/dcds.2010.28.1413
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