4 papers
A piecewise-linear fixed point theorem
David J. W. Simpson
We prove that if a continuous piecewise-smooth map on is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, th…
Three forms of dimension reduction for border-collision bifurcations
David J. W. Simpson
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes t…
Bifurcation analysis of multiple limit cycles created in boundary equilibrium bifurcations in hybrid systems
Hong Tang, Alan Champneys, David Simpson
A boundary equilibrium bifurcation (BEB) in a hybrid dynamical system occurs when a regular equilibrium collides with a switching surface in phase space. This causes a transition t…
The stability of fixed points on switching manifolds of piecewise-smooth continuous maps
David J. W. Simpson
This paper concerns piecewise-smooth maps on that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The st…