29 citations · 134 across the 16 of their papers we have counts for
18 papers
Mathematical analysis of a model for glycolytic oscillations in pancreatic -cells
Prannath Moolchand, Martin Wechselberger, Richard Bertram
Insulin secretion is pulsatile, with a period of about 5 min, coexisting with an ultradian rhythm (period of about 1 h), and a circadian (daily) rhythm. These rhythms are disrupted…
A coordinate-independent Pontryagin-Rodygin theorem for slow-fast averaging
Bob Rink, Theodore Vo, Martin Wechselberger
The slow drift along a manifold of periodic orbits is a key mathematical structure underlying bursting dynamics in many scientific applications. While classical averaging theory, a…
Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity
Thomas Miller, Alexander K. Y. Tam, Robert Marangell +2
Reaction-diffusion equations (RDEs) model the spatiotemporal evolution of a density field according to diffusion and net local changes. Usually, the diffusivity is p…
A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models
Bronwyn H Bradshaw-Hajek, Ian Lizarraga, Robert Marangell +1
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In t…
On the stability of isothermal shocks in black hole accretion disks
Eric W. Hester, Geoffrey M. Vasil, Martin Wechselberger
Most black holes possess accretion disks. Models of such disks inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study isot…
Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics
Samuel Jelbart, Nathan Pages, Vivien Kirk +2
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond…
Singularly Perturbed Boundary-Equilibrium Bifurcations
Samuel Jelbart, Kristian Uldall Kristiansen, Martin Wechselberger
Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB r…
Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion
Yifei Li, Peter van Heijster, Matthew J. Simpson +1
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, prolifera…
Multiple timescales and the parametrisation method in geometric singular perturbation theory
Ian Lizarraga, Bob Rink, Martin Wechselberger
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by t…
Singularly Perturbed Boundary-Focus Bifurcations
Samuel Jelbart, Kristian Uldall Kristiansen, Martin Wechselberger
We consider smooth systems limiting as to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable local normal form, we study the…
Contact singularities in nonstandard slow-fast dynamical systems
Ian Lizarraga, Robert Marangell, Martin Wechselberger
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form , and $\varepsilon\l…
Singularly Perturbed Oscillators with Exponential Nonlinearities
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan +1
Singular exponential nonlinearities of the form with small occur in many different applications. These terms have essential singularities for leading t…
Local theory for spatio-temporal canards and delayed bifurcations
Daniele Avitabile, Mathieu Desroches, Romain Veltz +1
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale s…
Computational singular perturbation method for nonstandard slow-fast systems
Ian Lizarraga, Martin Wechselberger
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since it…
Two-Stroke Relaxation Oscillators
Samuel Jelbart, Martin Wechselberger
Two-stroke relaxation oscillations consist of two distinct phases per cycle - one slow and one fast - which distinguishes them from the well-known van der Pol-type 'four-stroke' re…
Novel solutions for a model of wound healing angiogenesis
Kristen Harley, Peter van Heijster, Robert Marangell +2
We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In thi…
Numerical computation of an Evans function for travelling waves
K. Harley, P. v Heijster, R. Marangell +2
We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a…
Mixed mode oscillations in a conceptual climate model
Andrew Roberts, Esther Widiasih, Chris K. R. T. Jones +1
Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more compl…