Stochastic Resonance
in Nonlinear Signal Transmission 

Ph. D. Thesis of

Xavier Godivier

Decembre 3, 1997

LISA - Laboratoire d'Ingénierie des Systèmes Automatisés

University of Angers. 

Résumé en français / Esperanto-resumo

jury :

J.-P. Cocquerez, Professor, University of Cergy-Pontoise, President of the jury

C. Jutten, Professor, University J. Fourier, Report

P. Flandrin, Professor, Research Director, CNRS, Report

M. Guglielmi, Research Ingenieur CNRS, IRCyN, Examinator

J.-L. Ferrier, Professor, University of Angers, Examinator

F. Chapeau-Blondeau, Assistant Professor, University of Angers, Examinator and Advisor


The stochastic resonance is a nonlinear effect which consists of the possibility to improve the transmission of a useful signal by some nonlinear systems, by means of an increase of the noise in the system. One has elaborate a general formulation for the study of the periodic stochastic resonance, that unifies and includes preceding study results. This formulation is applied for the construction of a theory of the periodic stochastic resonance in a general class of nonlinear dynamic systems, in order that the signal noise report in exit can be increased by increasing the noise in entry. This theory is validated by means of numerical simulations and experiences with electronic circuits. It is also employed to demonstrate new conditions where the stochastic resonance can occur, as well as new properties. Then, one is interested then in the yet very new area of aperiodic stochastic resonance. One conceives new signals and system types that one demonstrate able of stochastic resonance, by supporting the analysis on statistical theory concepts of the information. One considers finally a class of natural systems realizing very effective nonlinear signal processing: the neuron systems. We show for the first time the stochastic resonance possibility, in the transmission by the neuron of signals in the form of spikes or trains of action potentials. 

french text available in PS(448 ko)

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