49 citations · 122 across the 17 of their papers we have counts for
7 papers · 1 filter
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…
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…