64 citations · 387 across the 46 of their papers we have counts for
48 papers
Refracting Filippov systems: sliding dynamics without sliding regions
D. J. W. Simpson
This paper develops fundamental mathematical theory for refracting Filippov systems. These are discontinuous ordinary differential equations with solutions defined in the sense of…
Extended normal forms for one-dimensional border-collision bifurcations
P. A. Glendinning, D. J. W. Simpson
The border-collision normal form describes the local dynamics in continuous systems with switches when a fixed point intersects a switching surface. For one-dimensional cases where…
Nonsmooth folds as tipping points
D. J. W. Simpson
A nonsmooth fold is where an equilibrium or limit cycle of a nonsmooth dynamical system hits a switching manifold and collides and annihilates with another solution of the same typ…
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…
Differentiable conjugacies for one-dimensional maps
P. A. Glendinning, D. J. W. Simpson
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topolo…
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…