33 citations · 98 across the 11 of their papers we have counts for
9 papers · 1 filter
Periodic orbits for square and rectangular billiards
Hongjia H. Chen, Hinke M. Osinga
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according…
Characterising blenders via covering relations and cone conditions
Maciej J. Capiński, Bernd Krauskopf, Hinke M. Osinga +1
We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditio…
Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study
Andrus Giraldo, Bernd Krauskopf, Hinke M. Osinga
We study a homoclinic flip bifurcation of case~\textbf{C}, where a homoclinic orbit to a saddle equilibrium with real eigenvalues changes from being orientable to nonorientable. Th…
Saddle Invariant Objects and their Global Manifolds in a Neighborhood of a Homoclinic Flip Bifurcation of Case B
Andrus Giraldo, Bernd Krauskopf, Hinke M. Osinga
When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes o…
Computing connecting orbits to infinity associated with a homoclinic flip bifurcation
Andrus Giraldo, Bernd Krauskopf, Hinke M. Osinga
We consider the bifurcation diagram in a suitable parameter plane of a quadratic vector field in that features a homoclinic flip bifurcation of the most complicated…
A continuation approach to computing phase resetting curves
Peter Langfield, Bernd Krauskopf, Hinke M. Osinga
Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief per…
Global manifold structure of a continuous-time heterodimensional cycle
Andy Hammerlindl, Bernd Krauskopf, Gemma Mason +1
A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work…
Quantitative modeling and analysis of bifurcation-induced bursting
J. E. Rubin, B. Krauskopf, H. M. Osinga
Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally…
Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment
M. Elmegård, B. Krauskopf, H. M. Osinga +2
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resul…