64 citations · 387 across the 46 of their papers we have counts for
5 papers · 2 filters
The stability of fixed points on switching manifolds of piecewise-smooth continuous maps
David J. W. Simpson
This paper concerns piecewise-smooth maps on that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The st…
Subsumed homoclinic connections and infinitely many coexisting attractors in piecewise-linear maps
David J. W. Simpson, Christopher P. Tuffley
We establish an equivalence between infinitely many asymptotically stable periodic solutions and subsumed homoclinic connections for -dimensional piecewise-linear continuous map…
Jitter in Dynamical Systems with Intersecting Discontinuity Surfaces
Mike R. Jeffrey, Georgios Kafanas, David J. W. Simpson
Mathematical models involving switches --- in the form of differential equations with discontinuities --- can accomodate real-world non-idealities through perturbations by hysteres…
The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations
D. J. W. Simpson
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a s…
Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps
David J. W. Simpson
The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, a…