Search Results - "Jelbart, Samuel"

Singularly perturbed boundary-focus bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…We consider smooth systems limiting as ϵ→0 to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable local normal…”
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Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems by Jelbart, Samuel

“…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…”
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Extending Discrete Geometric Singular Perturbation Theory to Non-Hyperbolic Points by Jelbart, Samuel, Kuehn, Christian

“…We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens…”
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A Formal Geometric Blow-up Method for Pattern Forming Systems by Jelbart, Samuel, Kuehn, Christian

“…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…”
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Discrete Geometric Singular Perturbation Theory by Jelbart, Samuel, Kuehn, Christian

“…We propose a mathematical formalism for discrete multi-scale dynamical systems induced by maps which parallels the established geometric singular perturbation…”
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Characterising exchange of stability in scalar reaction-diffusion equations via geometric blow-up by Jelbart, Samuel, Kuehn, Christian, Sánchez, Alejandro Martínez

“…We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities…”
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Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation by Jelbart, Samuel, Kristiansen, Kristian Uldall, Szmolyan, Peter

“…We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion…”
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Two-Stroke Relaxation Oscillators by Jelbart, Samuel, Wechselberger, Martin

“…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…”
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Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation by Hummel, Felix, Jelbart, Samuel, Kuehn, Christian

“…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…”
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Understanding broad-spike oscillations in a model of intracellular calcium dynamics by Rahmani, Behnaz, Jelbart, Samuel, Kirk, Vivien, Sneyd, James

“…Oscillations of free intracellular calcium concentration are thought to be important in the control of a wide variety of physiological phenomena, and there is…”
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Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems by Jelbart, Samuel, Kuehn, Christian, Kuntz, Sara-Viola

“…Journal of Nonlinear Science (2024) 34:17 Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary'…”
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Singularly Perturbed Boundary-Focus Bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…We consider smooth systems limiting as $\epsilon \to 0$ to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable…”
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Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics by Jelbart, Samuel, Pages, Nathan, Kirk, Vivien, Sneyd, James, Wechselberger, Martin

“…Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of…”
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Singularly Perturbed Boundary-Equilibrium Bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation…”
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Singularly Perturbed Oscillators with Exponential Nonlinearities by Jelbart, Samuel, Kristiansen, Kristian Uldall, Szmolyan, Peter, Wechselberger, Martin

“…Singular exponential nonlinearities of the form $e^{h(x)\epsilon^{-1}}$ with $\epsilon>0$ small occur in many different applications. These terms have…”
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