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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, 9, pp.469-485. ⟨hal-01277787⟩

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