Robustness of Turing patterns on networks

Abstract: Self-organising patterns originating from the Turing instability have been widely studied in the context of continuous media. One commonly studied question is how robust these Turing patterns are to a variety of external and internal changes to the underlying system and dynamics. More recently the extension of Turing’s work to the case of networks has been made, introducing the element of the network topology to Turing pattern formation. This introduces a new kind of robustness question, how robust are the developing patterns to changes in the network topology. We address this question by looking at pattern change under a bond percolation process. In this paper we also explain some of the theory of Turing patterns on networks, the parameter constraints needed for such patterns and its influence on the final long-time patterns that are observed.