29 citations · 60 across the 14 of their papers we have counts for
16 papers
Different Singular Limits in a Gene Regulatory Network with Multiple Small Parameters
Lukas Baumgartner, Samuel Jelbart
We consider a planar ODE system from an important class of models for gene regulatory dynamics. The system depends singularly on the steepness parameters $0<\varepsilon_1,\varepsil…
Switching, Multiple Time-Scales and Geometric Blow-Up in a Low-Dimensional Gene Regulatory Network
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan
ODE-based models for gene regulatory networks (GRNs) can often be formulated as smooth singular perturbation problems with multiple small parameters, some of which are related to t…
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…