Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions

TL;DR

This paper demonstrates that self-organized stationary patterns can form in networks of bistable chemical reactions through a mechanism alternative to Turing patterns, emphasizing the role of network structure and activation dynamics.

Contribution

It introduces a novel pattern formation mechanism in networked bistable systems, validated through experiments and applicable to various natural and engineered networks.

Findings

Pattern formation can be described by activation of domains.

Chemical reactions localize to network substructures.

Critical sites trigger system-wide activation.

Abstract

Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized stationary patterns. The results show that the pattern formation can be described by the identification of domains that can be activated individually or in combinations. The method also enabled the localization of chemical reactions to network substructures and the identification of critical sites whose activation results in complete activation of the system. Although the experiments were performed with a specific nickel electrodissolution system, they reproduced all the salient dynamic behavior of a general network model with a single nonlinearity parameter. Thus, the considered pattern-formation mechanism is very robust, and similar behavior can be expected in other natural or engineered networked systems that exhibit, at least locally, a treelike structure.