29 citations · 60 across the 14 of their papers we have counts for
4 papers · 2 filters
Characterising exchange of stability in scalar reaction-diffusion equations via geometric blow-up
Samuel Jelbart, Christian Kuehn, Alejandro Martínez Sánchez
We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities in the reaction term,…
Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan
We prove the existence of a family of travelling wave solutions in a variant of the , a reaction-diffusion equation which model…
Understanding broad-spike oscillations in a model of intracellular calcium dynamics
Behnaz Rahmani, Samuel Jelbart, Vivien Kirk +1
Oscillations of free intracellular calcium concentration are thought to be important in the control of a wide variety of physiological phenomena, and there is long-standing interes…
Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems
Samuel Jelbart
This work provides a geometric approach to the study of bifurcation and rate induced transitions in a class of non-autonomous systems referred to herein as $\textit{asymptotically…