64 citations · 387 across the 46 of their papers we have counts for
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math.DS2018
Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems
David J. W. Simpson
This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stab…
math.DS2018★ 37 cited
A Compendium of Hopf-Like Bifurcations in Piecewise-Smooth Dynamical Systems
D. J. W. Simpson
This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium bifur…
math.DS2018★ 2 cited
Dimension reduction for slow-fast, piecewise-smooth, continuous systems of ODEs
David J. W. Simpson
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, su…