83 citations · 130 across the 10 of their papers we have counts for
8 papers · 1 filter
A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models
Bronwyn H Bradshaw-Hajek, Ian Lizarraga, Robert Marangell +1
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In t…
Nonlinear stability of shock-fronted travelling waves under nonlocal regularization
Ian Lizarraga, Robert Marangell
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied b…
Spectral stability of shock-fronted travelling waves under viscous relaxation
Ian Lizarraga, Robert Marangell
Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Yi et. al. (2021) has demonstrated the existence of s…
Multiple timescales and the parametrisation method in geometric singular perturbation theory
Ian Lizarraga, Bob Rink, Martin Wechselberger
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by t…
Contact singularities in nonstandard slow-fast dynamical systems
Ian Lizarraga, Robert Marangell, Martin Wechselberger
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form , and $\varepsilon\l…
Computational singular perturbation method for nonstandard slow-fast systems
Ian Lizarraga, Martin Wechselberger
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since it…
Tangency bifurcation of invariant manifolds in a slow-fast system
Ian Lizarraga
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repel…
Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations
John Guckenheimer, Ian Lizarraga
The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process. Koper and Gaspard described par…