9 papers
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…
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…