Showing math.DSShow all
3 papers · 1 filter
math.DS2021
The Geometry of the Painlevé paradox
Noah Cheesman, S. John Hogan, Kristian Uldall Kristiansen
Painlevé showed that there can be inconsistency and indeterminacy in solutions to the equations of motion of a 2D rigid body moving on a sufficiently rough surface. The study of Pa…
math.DS2021
Regularisation of isolated codimension-2 discontinuity sets
Noah Cheesman, Kristian Uldall Kristiansen, S. J. Hogan
Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to syst…
math.DS2012
Stochastic Regular Grazing Bifurcations
David J. W. Simpson, S. J. Hogan, Rachel Kuske
A grazing bifurcation corresponds to the collision of a periodic orbit with a switching manifold in a piecewise-smooth ODE system and often generates complicated dynamics. The lowe…