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Canard solutions and bifurcations in smooth models of plane structure variable systems

Abstract : 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.
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Luis Gonzaga Albuquerque. Canard solutions and bifurcations in smooth models of plane structure variable systems. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008, pp.469-485. ⟨10.46298/arima.1915⟩. ⟨hal-01277787⟩

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