Chaos in the hysteretic grazing-sliding codimension-one saddle-node bifurcation of piecewise dynamical systems
Document typeConference lecture
PublisherUP4, Institute of Sciences, S.L.
Rights accessOpen Access
We present two ways of regularizing a parameter family of piecewise smooth dynamical systems undergoing a grazing- sliding bifurcation. We use the Sotomayor-Teixeira regularization and prove that the bifurcation is a saddle-node (see [ ? ]). Then we perform a hysteretic regularization. However, in spite that the two regularization will give the same dynamics in the sliding modes (see [ ? ]), when a tangency appears, so is in the case of grazing-sliding, the hysteretic process generate chaotic dynamics. Finally, we smooth the hysteresis by embedding the system in a higher dimension. Now the discontinuous control variable u is also a continuous time dependent variable although a fast-fast one. We then encounter loop feedback chaotic behaviour
CitationBonet, C., Martinez-seara, T. Chaos in the hysteretic grazing-sliding codimension-one saddle-node bifurcation of piecewise dynamical systems. A: Congreso de Ecuaciones Diferenciales y Aplicaciones y Congreso de Matemàtica Aplicada. "CEDYA 2017 - Communications Book". UP4, Institute of Sciences, S.L., 2017, p. 73-77.