Piecewise linear systems and slow-fast dynamics related to Hopf-like bifurcations
Present day, piecewise linear (PWL) systems have become an extended toolin order to tackle some dynamical issues. For instance, PWL systems have provento be useful to provide salient features of smooth systems while being moreamenable to theoretical and computational analysis. Further, they are widelyused in slow-fast dynamics, which are related with canard phenomena orslow-passage phenomena. In particular, the slow-passage phenomena arecharacterized in slow-fast differential systems as changing behavior presentedby the corresponding orbit when it crosses a bifurcation point near a slowmanifold. These phenomena are widely known in the field of dynamical systemsand they are used to understand some qualitative and quantitative aspectsappearing in some slow-fast differential systems, such as complex oscillations.Hence, in this talk, we made an introduction of PWL systems and finally, we aimto see, for the first time, that the slow-passage phenomena can be alsoobserved in PWL system. In particular, we present which conditions, in terms ofnumber of linearity regions, a PWL slow-fast system has to exhibit to be ableto reproduce this phenomenon through a Hopf-like bifurcation.