101 citations · 509 across the 34 of their papers we have counts for
19 papers · 1 filter
Bifurcation analysis of a conceptual model for the Atlantic Meridional Overturning Circulation
John Bailie, Bernd Krauskopf
The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and salt into the Northern Hemisphere via a warm surface current toward the subpolar North Atlantic, where w…
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…
Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop
Antony R. Humphries, Bernd Krauskopf, Stefan Ruschel +1
We study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduc…
Bifurcation Analysis of Systems with Delays: Methods and Their Use in Applications
Bernd Krauskopf, Jan Sieber
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example…
Signatures consistent with multi-frequency tipping in the Atlantic meridional overturning circulation
Andrew Keane, Bernd Krauskopf, Timothy M. Lenton
The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly a…
The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback
Stefan Ruschel, Bernd Krauskopf, Neil G. R. Broderick
We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber, and study the effects of delayed optical self-feedback in the excitable case. More sp…
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…
The Yamada model for a self-pulsing laser: bifurcation structure for non-identical decay times of gain and absorber
Robert Otupiri, Bernd Krauskopf, Neil G. R. Broderick
We consider self-pulsing in lasers with a gain section and an absorber section via a mechanism known as Q-switching, as described mathematically by the Yamada ordinary differential…
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…
Resonance phenomena in a scalar delay differential equation with two state-dependent delays
R. C. Calleja, A. R. Humphries, B. Krauskopf
We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and…
Effects of time-delay in a model of intra- and inter-personal motor coordination
Piotr Słowiński, Krasimira Tsaneva-Atanasova, Bernd Krauskopf
Motor coordination is an important feature of intra- and inter-personal interactions, and several scenarios --- from finger tapping to human-computer interfaces --- have been inves…
Bifurcation analysis of delay-induced resonances of the El-Nino Southern Oscillation
Bernd Krauskopf, Jan Sieber
Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the…
Using feedback control and Newton iterations to track dynamically unstable phenomena in experiments
Jan Sieber, Bernd Krauskopf
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamic…