Stability of rotating wave solutions in reaction-diffusion systems with nonlocal interaction on a circle

This paper investigates the stability of rotating waves in a class of reaction–diffusion systems with nonlocal interactions on a circular domain. We establish the existence of a center manifold and derive conditions ensuring the existence of rotating waves on this manifold. Their stability is characterized through the computation of characteristic exponents associated with the reduced dynamics on the center manifold. The theoretical framework is applied to two representative model systems, and numerical simulations are presented to corroborate the analytical predictions.