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math.DS2026
Grazing bifurcations of linear impact oscillators in the zero damping limit
Olivia J. Goodman, David J. W. Simpson
We consider a harmonically forced linear impact oscillator, where impact events are instantaneous with energy loss. We study the dynamics at the grazing bifurcation of the non-impa…
math.DS2026
Resonant grazing bifurcations revisited
David J. W. Simpson, Indranil Ghosh
In vibro-impact mechanics, the division between an impact and a near miss is a zero-velocity grazing event. Grazing bifurcations of stable periodic motions often produce complicate…
math.DS2025
The VIVID function for numerically continuing periodic orbits arising from grazing bifurcations of hybrid dynamical systems
Indranil Ghosh, David J. W. Simpson
Periodic orbits of systems of ordinary differential equations can be found and continued numerically by following fixed points of Poincaré maps. However, this often fails near gra…