64 citations · 387 across the 46 of their papers we have counts for
6 papers · 2 filters
Robust Devaney chaos in the two-dimensional border-collision normal form
Indranil Ghosh, David J. W. Simpson
The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on can be reduced to a four-parameter family known as the two-dimensional border-c…
Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters
David J. W. Simpson, Paul A. Glendinning
The dynamics near a border-collision bifurcation are approximated to leading order by a continuous, piecewise-linear map. The purpose of this paper is to consider the higher-order…
Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells
H. O. Fatoyinbo, R. G. Brown, D. J. W. Simpson +1
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurca…
Unfolding globally resonant homoclinic tangencies
Sishu Shankar Muni, Robert I. McLachlan, David J. W. Simpson
Global resonance is a mechanism by which a homoclinic tangency of a smooth map can have infinitely many asymptotically stable, single-round periodic solutions. To understand the bi…
Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones
P. A. Glendinning, D. J. W. Simpson
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tange…
On the stability of boundary equilibria in Filippov systems
David J. W. Simpson
The leading-order approximation to a Filippov system about a generic boundary equilibrium is a system that is affine one side of the boundary and constant on the othe…