64 citations · 387 across the 46 of their papers we have counts for
Showing 2013 · math.DSShow all
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math.DS2013★ 23 cited
Sequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form
David J. W. Simpson
The border-collision normal form is a piecewise-linear continuous map on that describes dynamics near border-collision bifurcations of nonsmooth maps. This paper stu…
math.DS2013★ 1 cited
Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise
Mike R. Jeffrey, David J. W. Simpson
Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth function…
math.DS2013
On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations
David J. W. Simpson
A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double…