Luis Gonzaga Albuquerque - Canard solutions and bifurcations in smooth models of plane structure variable systems

arima:1915 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, October 16, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 - https://doi.org/10.46298/arima.1915
Canard solutions and bifurcations in smooth models of plane structure variable systems

Authors: Luis Gonzaga Albuquerque

Systems that operate in different modes with quick transition are usually studied through discontinuous systems. We give a model of a smoothing of the transition between two vector fields along a separation line, allowing perturbations of the vector fields and of the separation line. In this model there appears a canard phenomenon in certain macroscopically indeterminate situations. This phenomenon gives a new point of view on some situations usually studied through discontinuous bifurcations. We also study the dynamics near the transition line through an associated slow-fast system and compare the slow dynamics with the classical theory, namely, sliding mode dynamics in variable structure systems and equivalent control.


Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008
Published on: October 16, 2008
Submitted on: March 25, 2008
Keywords: discontinuous bifurcations., sliding mode dynamics, equivalent control, slow-fast systems, nonstandard analysis,Canards,systèmes lent-rapides,analyse non standard,mouvement glissant,contrôle équivalent,bifurcations discontinues,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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