Persistent homology classifies parameter dependence of patterns in Turing systems

TL;DR

This paper applies topological data analysis to reaction-diffusion systems, showing that persistent homology can classify how pattern topology depends on system parameters, aiding in parameter estimation.

Contribution

It demonstrates the use of persistent homology to analyze parameter dependence of patterns in Turing systems, with practical clustering methods for biological and chemical models.

Findings

Topological summaries reveal parameter-dependent pattern changes.

Clustering algorithms identify distinct pattern topologies.

Application to biological systems demonstrates practical utility.

Abstract

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter dependence of pattern topology in reaction diffusion systems, by examining the homology of sublevel sets of solutions to Turing reaction diffusion systems for a range of parameters. We demonstrate that a topological clustering algorithm can reveal how pattern topology depends on parameters, using the chlorite--iodide--malonic acid system, and the prototypical Schnakenberg system for illustration. In addition, we discuss the prospective application of such clustering, for instance in refining priors for detailed parameter estimation for self-organising systems.