Persistent Homology Classifies Parameter Dependence of Patterns in Turing Systems

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.