Extending stochastic resonance for neuron models to general Levy noise

Applebaum, D. (2009) Extending stochastic resonance for neuron models to general Levy noise. IEEE Transactions on Neural Networks, 20 (12). pp. 1993-1995. ISSN 1045-9227

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Abstract

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Levy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general Levy noise models. We achieve this by showing that ¿large jump¿ discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a ¿forbidden intervals¿ theorem as in Patel and Kosko's paper.

Item Type:	Article
Copyright, Publisher and Additional Information:	© Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords:	Levy noise; neuron models; stochastic differential equation (SDE); stochastic resonance (SR)
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Mrs Megan Hobbs
Date Deposited:	22 Mar 2010 11:28
Last Modified:	08 Feb 2013 17:00
Published Version:	http://dx.doi.org/10.1109/TNN.2009.2033183
Status:	Published
Publisher:	Institute of Electrical and Electronics Engineers
Identification Number:	10.1109/TNN.2009.2033183
URI:	http://eprints.whiterose.ac.uk/id/eprint/10603

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