Spatiotemporal pattern formation in a three-variable CO oxidation reaction model

TL;DR

This paper investigates how spatiotemporal patterns emerge in a CO oxidation model on Pt(110) surfaces, revealing conditions for Turing and Hopf bifurcations leading to spatial, temporal, or combined patterns.

Contribution

It demonstrates that non-autocatalytic CO oxidation systems can exhibit Turing and Hopf bifurcations, leading to diverse pattern formations, which was previously unestablished.

Findings

Conditions for Turing bifurcation are analytically derived.

Conditions for Hopf bifurcation are analytically derived.

Spatiotemporal patterns are observed under combined bifurcation scenarios.

Abstract

The spatiotemporal pattern formation is studied in the catalytic carbon monoxide oxidation reaction that takes into account the diffusion processes over the Pt(110) surface, which may contain structurally different areas. These areas are formed during CO-induced transition from a reconstructed phase with $1\times2$ geometry of the overlayer to a bulk-like ($1\times1$) phase with square atomic arrangement. Despite the CO oxidation reaction being non-autocatalytic, we have shown that the analytic conditions of the existence of the Turing and the Hopf bifurcations can be satisfied in such systems. Thus, the system may lose its stability in two ways --- either through the Hopf bifurcation leading to the formation of temporal patterns in the system or through the Turing bifurcation leading to the formation of regular spatial patterns. At a simultaneous implementation of both scenarios, spatiotemporal patterns for CO and oxygen coverages are obtained in the system.