Bifurcation analysis of dynamic systems with continuously piecewise linearity

Abstract

The periodic response and associated bifurcations of a harmonically driven oscillator with continuously piecewise linearity has received great attention during the past decade. The oscillator serves as a widely used model to describe various mechanical systems with clearances, elastic constraints etc. Even if the 'corners' of the piecewise-linear restoring force in the oscillator make the system non-smooth on the interface between two linear regions, the bifurcation analysis published up to now is still based on the theory of smooth dynamic systems. The validity of such an extention is an open problem.