Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells

TL;DR

This paper investigates how wave front propagation fails in coupled nonlinear systems, revealing a universal exponential scaling of the critical field with coupling strength, applicable across various scientific domains.

Contribution

Introduces a new generic method to analyze the scaling of propagation failure in coupled nonlinear cells, demonstrating universal exponential behavior across different coupling regimes.

Findings

Critical external field scales exponentially with coupling strength.

Propagation failure occurs universally at a predictable threshold.

Method validated through numerical simulations.

Abstract

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings, and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.