64 citations · 387 across the 46 of their papers we have counts for
6 papers · 1 filter
Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps
Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applic…
Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form
P. A. Glendinning, D. J. W. Simpson
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic att…
A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters
Hammed Olawale Fatoyinbo, David J. W. Simpson
The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper we provide a guide to the dynamics of this f…
Renormalisation of the two-dimensional border-collision normal form
Indranil Ghosh, David J. W. Simpson
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on ) in the robust chaos parameter region of […
Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
D. J. W. Simpson, J. D. Meiss
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and…
Andronov-Hopf Bifurcations in Planar, Piecewise-Smooth, Continuous Flows
D. J. W. Simpson, J. D. Meiss
An equilibrium of a planar, piecewise-, continuous system of differential equations that crosses a curve of discontinuity of the Jacobian of its vector field can undergo a num…