# A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

## TL;DR

This paper introduces a unified theoretical framework based on response functions to analyze the drift and dynamics of spiral and meandering waves in oscillatory and excitable systems under small external perturbations.

## Contribution

It develops a comprehensive response function approach that accounts for spiral wave meander and finite tip radius, enabling prediction of pattern drift in various coordinate systems.

## Key findings

- Framework accurately predicts spiral wave drift under external fields.
- Accounts for spiral wave meander and finite tip radius.
- Applicable to different coordinate systems for analysis.

## Abstract

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearised operator (i.e. `response functions'). For spiral waves, the finite radius of the spiral tip trajectory as well as spiral wave meander are taken into account. Different coordinates systems can be chosen, depending on whether one wants to predict the motion of the spiral wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyse the drift of a meandering spiral wave in a constant external field in different regimes.