# American Institute of Mathematical Sciences

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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

 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.
Citation: Per Danzl, Ali Nabi, Jeff Moehlis. Charge-balanced spike timing control for phase models of spiking neurons. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1413-1435. doi: 10.3934/dcds.2010.28.1413
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