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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…
A Formal Geometric Blow-up Method for Pattern Forming Systems
Samuel Jelbart, Christian Kuehn
We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far o…
Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation
Felix Hummel, Samuel Jelbart, Christian Kuehn
We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-Hohenberg equation using a novel approach based on geometric blow-up. We show that the…