Journal Article

Optimal control of input rates of Stein's models

Lili Lu

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 28, issue 1, pages 31-46
Published in print March 2011 | ISSN: 1477-8599
Published online April 2010 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqq004
Optimal control of input rates of Stein's models

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We investigate the optimal control of neuronal spiking activity for classical Stein's model, Stein's model with reversal potentials with continuous random inputs, characterized by a positive parameter α and Stein's model with Poisson inputs. We solve the optimal control problems and obtain optimal rates λ(t) for different kinds of models. The numerical simulations on variable parameters show that it is possible to make the interval of spikes the same as our expected time in the range of the values of parameters.

Keywords: reversal potential; maximum principle; stopping time; Poisson process; Ornstein–Uhlenbeck process

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Subjects: Applied Mathematics ; Biomathematics and Statistics

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