6 papers
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…
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…
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 graz…
Robust chaos in
Indranil Ghosh, David J. W. Simpson
We treat -dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions f…
The two-dimensional border-collision normal form with a zero determinant
David J. W. Simpson
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece…
The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps
Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attracto…