64 citations · 387 across the 46 of their papers we have counts for
4 papers · 2 filters
Unfolding codimension-two subsumed homoclinic connections in two-dimensional piecewise-linear maps
David J. W. Simpson
For piecewise-linear maps, the phenomenon that a branch of a one-dimensional unstable manifold of a periodic solution is completely contained in its stable manifold is codimension-…
Robust Chaos and the Continuity of Attractors
Paul A. Glendinning, David J. W. Simpson
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We…
Constructing robust chaos: invariant manifolds and expanding cones
Paul A. Glendinning, David J. W. Simpson
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been e…
Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems
David J. W. Simpson
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thre…