Work

Propagation reversal on trees in the large diffusion regime

Year: 2024

Type: article

Abstract: In this work we study travelling wave solutions to bistable reaction–diffusion equations on bi-infinite k -ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction–diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formulas to bound the thin region in parameter space where the propagation direction undergoes a reversal.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2024.100468

Authors: Hermen Jan Hupkes, Mia Jukić

Institutions: Leiden University, Netherlands Organisation for Applied Scientific Research

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,490

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek