49 citations · 122 across the 17 of their papers we have counts for
19 papers
Pushed and pulled fronts in a logistic Keller-Segel model with chemorepulsion
Montie Avery, Matt Holzer, Arnd Scheel
We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbat…
Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization
Matt Holzer, Matthew Kearney, Samuel Molseed +2
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infini…
Pushed-to-pulled front transitions: continuation, speed scalings, and hidden monotonicity
Montie Avery, Matt Holzer, Arnd Scheel
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show…
Pattern Formation in Random Networks Using Graphons
Jason Bramburger, Matt Holzer
We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our appr…
Epidemic spreading on complex networks as front propagation into an unstable state
Ashley Armbruster, Matt Holzer, Noah Roselli +1
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion front…
Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity
Grégory Faye, Thomas Giletti, Matt Holzer
We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coeffic…
Invasion into remnant instability: a case study of front dynamics
Gregory Faye, Matt Holzer, Arnd Scheel +1
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant insta…
Locked fronts in a discrete time discrete space population model
Matt Holzer, Zachary Richey, Wyatt Rush +1
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exh…
Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model
Gregory Faye, Matt Holzer
We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front…
Asymptotic stability of the critical Fisher-KPP front using pointwise estimates
Gregory Faye, Matt Holzer
We propose a simple alternative proof of a famous result of Gallay regarding the nonlinear asymptotic stability of the critical front of the Fisher-KPP equation which shows that pe…
Estimating epidemic arrival times using linear spreading theory
Lawrence M. Chen, Matt Holzer, Anne Shapiro
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is com…
Pattern formation, traveling fronts and consensus versus fragmentation in a model of opinion dynamics
Matt Holzer, Ratna Khatri
We consider a continuous version of the Hegselmann-Krause model of opinion dynamics. Interaction between agents either leads to a state of consensus, where agents converge to a sin…
Bifurcation to locked fronts in two component reaction-diffusion systems
Gregory Faye, Matt Holzer
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the ex…
Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs
Aaron Hoffman, Matt Holzer
We study the dynamics of the Fisher-KPP equation on the infinite homogeneous tree and Erdős-Réyni random graphs. We assume initial data that is zero everywhere except at a single n…
Linear spreading speeds from nonlinear resonant interaction
Gregory Faye, Matt Holzer, Arnd Scheel
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such r…
A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations
Matt Holzer
This article is concerned with the rigorous validation of anomalous spreading speeds in a system of coupled Fisher-KPP equations of cooperative type. Anomalous spreading refers to…
Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach
Gregory Faye, Matt Holzer
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied the system undergoes a Turing bifurcation. We study the dynamics…
Criteria for pointwise growth and their role in invasion processes
Matt Holzer, Arnd Scheel
This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth…
Anomalous spreading in a system of coupled Fisher-KPP equations
Matt Holzer
In this article, we report on the curious phenomena of anomalous spreading in a system of coupled Fisher-KPP equations. When a single parameter is set to zero, the system consists…