Analyzing Pattern Formation in the Gray--Scott Model: An XPPAUT Tutorial

Abstract

The Gray-Scott model is a widely-studied autocatalytic model that exhibits a range of interesting pattern formation behaviour, as well as a rich structure of dynamics that includes many ideas from a typical undergraduate dynamical systems course, and some from beyond. Understanding the solutions to this model is arguably most easily conducted via a bifurcation analysis of corresponding ODE problems within the software XPPAUT. In this paper, we provide an introductory XPPAUT tutorial, through which we begin to expose the range of intricate patterns that the Gray-Scott model emits.

Platelet-Driven Routes to Chaos in a Model of Hepatitis

“…We therefore focus our analysis upon numerical simulation of the model in Matlab (using standard ODE solvers such as ode45) and bifurcation analysis conducted in XPPAUT. The latter of these uses continuation methods to track the model's steady state and periodic solutions as model parameters are varied, as described in [6]. We highlight that all of the Matlab and XPPAUT codes used in this article have been made available online at https://github.com/ martinrnelson/PlateletChaosHepatitis.…”