5 papers · 1 filter
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…
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…
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…
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…