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

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic 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 linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate 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 analyze the drift of a meandering spiral wave in a constant external field in different regimes. © 2019 authors. Published by the American Physical Society.This research was supported in part the EPSRC Grants No. EP/E018548/1, EP/D074789/1, EP/P008690/1, EP/N014391/1, and EP/E016391/1 (UK), National Science Foundation Grants No. NSF PHY-1748958, NIH Grant No. R25GM067110, and the Gordon and Betty Moore Foundation Grant No. 2919.01 (USA)