Front motion and localized states in an asymmetric bistable activator-inhibitor system with saturation

TL;DR

This paper investigates the dynamics of fronts and localized states in an asymmetric bistable activator-inhibitor system with saturation, revealing two distinct pinning regions and bifurcations affecting pattern formation.

Contribution

It identifies two types of pinning regions in a saturated activator-inhibitor model and analyzes their bifurcations, expanding understanding of pattern formation in biological systems.

Findings

Two distinct pinning regions identified in the model.

Heteroclinic bifurcation separates parameter regions of counterpropagating fronts.

Activator domain retraction suggests potential therapeutic strategies.

Abstract

We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry. Using the Gierer-Meinhardt prototype model, we find the conditions in which two distinct pinning regions are formed. The first pinning type is known in the context of variational systems while the second is structurally different due to the presence of a heteroclinic bifurcation between two uniform states. The bifurcation also separates the parameter regions of counterpropagating fronts, leading in turn to the growth or contraction of activator domains. These phenomena expand the range of pattern formation theory and its biomedical applications: activator domain retraction suggests potential therapeutic strategies for patterned pathologies, such as cardiovascular calcification.