Noise-driven loss of chimera states and bifurcations in a nonlocal oscillator ring

Abstract

Independent phase noise can remove the spatial contrast of a chimera while leaving substantial collective coherence. We study this transition in a nonlocally coupled Kuramoto--Sakaguchi ring with a cosine kernel using the nonlinear Fokker--Planck equation. Stationary self-consistency and spatial spectra identify two bifurcations of the uniform ordered state at a reference phase lag. A symmetry-aware amplitude reduction distinguishes a subcritical lower endpoint $D_l$ from a supercritical upper endpoint $D_u$ and shows that reconstruction of the collective rotation frequency is essential to obtain the cubic coefficient. The upper endpoint admits a nonequilibrium Landau-type description of continuous spatial translation-symmetry restoration. Direct integration confirms stationary modulation below the upper threshold, algebraic relaxation at criticality, and exponential decay toward uniform partial synchronization above it. Continuation in noise intensity and phase lag resolves finite-amplitude saddle nodes, a narrow cusp, and a distinct cubic-zero point with a positive quintic coefficient. Together, these results connect the bifurcation structure of noisy chimera branches to spatial symmetry restoration and critical relaxation.