Stability of localized wave fronts in bistable systems

TL;DR

This paper investigates the conditions and stability of localized wave fronts in bistable biological systems influenced by self-activation, degradation, and spatial signals, revealing key factors that enhance stability.

Contribution

It provides a comprehensive analysis of wave-front localization conditions and stability criteria in bistable models with inhomogeneous activation and noise.

Findings

Stability improves when regulating positional signals.

Low binding cooperativity can enhance wave-front stability.

Self-activation impacts destabilization sources differently.

Abstract

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization.