3 papers
math.DS2026
The stability of boundary equilibria of three-dimensional Filippov systems
David J. W. Simpson
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equil…
math.DS2025
From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of maps
D. J. W. Simpson, V. Avrutin
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show…
math.DS2024
A piecewise-linear fixed point theorem
David J. W. Simpson
We prove that if a continuous piecewise-smooth map on is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, th…