On the asymptotic wavenumber of spiral waves in $\lambda-\omega$ systems

TL;DR

This paper investigates spiral wave solutions in a broad class of $\lambda-\omega$ systems, demonstrating that their asymptotic wavenumber smoothly depends on a small perturbation parameter.

Contribution

It proves that the asymptotic wavenumber of spiral waves is a $\mathcal{C}^{\infty}$-flat function of the perturbation parameter $q$ in $\lambda-\omega$ systems.

Findings

Asymptotic wavenumber is a $\mathcal{C}^{\infty}$-flat function of $q$

The result applies to a general class of $\lambda-\omega$ systems

Provides a rigorous mathematical proof of the smooth dependence

Abstract

In this paper we consider spiral wave solutions of a general class of $\lambda-\omega$ systems with a small parameter $q$ and we prove that the asymptotic wavenumber of the spirals is a $\mathcal{C}^{\infty}$-flat function of the perturbation parameter $q$.