AULA - Collegezaal C Live Meeting
Jul 23, 2024 14:00 - 15:20(Europe/Amsterdam)
20240723T1400 20240723T1520 Europe/Amsterdam MS03.4: Computational Methods AULA - Collegezaal C Enoc2024 n.fontein@tudelft.nl
23 attendees saved this session
A Boundary-Value Problem Approach to Computing Isochrons of Higher-Dimensional OscillatorsView Abstract
MS-03 - Computational Methods 02:00 PM - 02:20 PM (Europe/Amsterdam) 2024/07/23 12:00:00 UTC - 2024/07/23 12:20:00 UTC
The phase shift of an oscillator in response to an external stimulus has been used to characterise, understand and predict biological behaviours. Such phase shifts are studied mathematically by first modelling the oscillator as an attracting periodic orbit, and then considering its isochrons. Each isochron is an (n − 1)-dimensional submanifold defined as the set of points in the basin of attraction whose trajectories converge to the oscillator with the same phase. While methods exist to compute one- and even two-dimensional isochrons, the dimension of isochrons of biological models that motivate their computation are often much higher. One approach to this problem is to restrict the space of interest to points perturbed away from the periodic orbit for a perturbation with fixed form but where the amplitude and phase of application may vary. The slices of isochron that exist in this two-dimensional subspace are generally one-dimensional curves. We present our method to compute isochron slices via the continuation of a two-point boundary-value problem that relates the phase of a point resulting from a perturbation, with the amplitude of the perturbation and the phase in the cycle at which it is applied. We demonstrate our approach by computing isochrons of the four-dimensional Hodgkin–Huxley model, where we are able to resolve intricate geometrical detail.
Presenters
PL
Peter Langfield
Researcher, INRIA
Co-Authors
BK
Bernd Krauskopf
Professor, University Of Auckland
HO
Hinke M. Osinga
Professor, University Of Auckland
Isochron Geometry and its Influence on the Phase Resetting for Planar Oscillatory SystemsView Abstract
MS-03 - Computational Methods 02:20 PM - 02:40 PM (Europe/Amsterdam) 2024/07/23 12:20:00 UTC - 2024/07/23 12:40:00 UTC
Phase resetting investigates oscillatory systems by quantifying the phase shift between a point on a stable periodic orbit and its return position following a perturbation. While this approach is applicable to numerical simulations of mathematical models, computing phase resets with high precision poses challenges. We employ a recently developed high-precision computational method based on the numerical continuation of a multi-segment boundary value problem to compute phase resets. We focus on phase reset resulting from fixed perturbation amplitude applied at a fixed phase, while the perturbation angle varies. We call the graph of the map that relates the perturbation angle with the new phase the dircetional transition curve and show how characteristics of this map and curve changes as the perturbation amplitude increases. We illustrate our findings with the FitzHugh-Nagumo system.
Presenters
KL
Kyoung Hyun Lee
Researcher, University Of Auckland
Co-Authors
NB
Neil Broderick
Professor, University Of Auckland
BK
Bernd Krauskopf
Professor, University Of Auckland
HO
Hinke M. Osinga
Professor, University Of Auckland
Entropic transfer operatorsView Abstract
MS-03 - Computational Methods 02:40 PM - 03:00 PM (Europe/Amsterdam) 2024/07/23 12:40:00 UTC - 2024/07/23 13:00:00 UTC
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analysed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the n-torus and show three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.
Presenters
OJ
Oliver Junge
Professor, Technical University Of Munich
Towards infinity and beyond: homoclinic flip bifurcation and connecting orbits to infinityView Abstract
MS-03 - Computational Methods 03:00 PM - 03:20 PM (Europe/Amsterdam) 2024/07/23 13:00:00 UTC - 2024/07/23 13:20:00 UTC
We present an implementation of Lin's method to compute codimension-one heteroclinic connections to infinity. Furthermore, we show how these heteroclinic bifurcations with infinity organise the limiting behaviour of a family of codimension-one homoclinic bifurcations that emanates from a codimension-two homoclinic flip bifurcation.
Presenters
AG
Andrus Giraldo
Research Fellow, Korean Institute For Advanced Study
Co-Authors
BK
Bernd Krauskopf
Professor, University Of Auckland
HO
Hinke M. Osinga
Professor, University Of Auckland
Research Fellow
,
Korean Institute For Advanced Study
Professor
,
Technical University Of Munich
Researcher
,
University Of Auckland
Researcher
,
INRIA
Assistant Professor
,
NC State University
Dr. Behrooz Yousefzadeh
Associate Professor
,
Concordia University
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Towards infinity and beyond: homoclinic flip bi...
1705894627GKO_CInfty_ENOC2024.pdf View Download Presentation Submitted by Andrus Giraldo 4
Entropic transfer operators
1713785271enoc2024_latex_template.pdf View Download Presentation Submitted by Oliver Junge 4
Isochron Geometry and its Influence on the Phas...
1712808509enoc2024_LBKO_phase_reset.pdf View Download Presentation Submitted by Kyoung Hyun Lee 3
A Boundary-Value Problem Approach to Computing ...
1705309651enoc2024_Langfield.pdf View Download Presentation Submitted by Peter Langfield 5
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