TY - CONF
AU - Bonet, C.
AU - Martinez-seara, Tere
T3 - XXV CONGRESO DE ECUACIONES DIFERENCIALES Y APLICACIONES / XV CONGRESO DE MATEMÁTICA APLICADA
PY - 2017
Y1 - 2017
SP - 73
EP - 77
PB - UP4, Institute of Sciences, S.L.
UR - http://up4sciences.org/bookdetails/
AB - 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
T2 - Congreso de Ecuaciones Diferenciales y Aplicaciones y Congreso de Matemàtica Aplicada
TI - Chaos in the hysteretic grazing-sliding codimension-one saddle-node bifurcation of piecewise dynamical systems
ER -