Non-Smooth Bifurcations in Electronic

Abstract

One-parameter nonsmooth bifurcations occur in piecewise-smooth sets of ordinary differential equations. Motivated by applications, ‘bifurcation’ is defined as a nonsmooth transition with respect to a codimension-one discontinuity boundary in phase space. Only local bifurcations are considered, involving equilibria or a single point of boundary interaction along a limit cycle. Filippov systems are specially considered because its application in electronic circuits, as power electronic converters. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors and bifurcation diagrams with sharp corners. An example of a variable structure circuit, which is a first step in designing a DC-DC converter, is studied with some detail.