Extended normal forms for one-dimensional border-collision bifurcations

Abstract Border-collision bifurcations occur in switched dynamical systems when a fixed point hits a switching manifold under parameter variation. A standard way to analyse border-collision bifurcations is with a piecewise-linear normal form, as this is often topologically conjugate to the original system. In this paper we show how a stronger differentiable conjugacy can be achieved for one-dimensional border-collision bifurcations by using an extended normal form.