101 citations · 509 across the 34 of their papers we have counts for
7 papers · 1 filter
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…
Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback
Soizic Terrien, Bernd Krauskopf, Neil G. R. Broderick +6
Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external p…
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…
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing
Carlo R. Laing, Bernd Krauskopf
We consider a single theta neuron with delayed self-feedback in the form of a Dirac delta function in time. Because the dynamics of a theta neuron on its own can be solved explicit…