Spontaneous alternation of rotating phase waves in a nonlinear oscillator ring driven by heterogeneity

We report the spontaneous alternation of rotating phase waves in a ring of reactively coupled nonlinear oscillators with heterogeneity. In contrast to uniform systems that support unidirectional phase rotation, heterogeneity can induce periodic alternation between clockwise and counterclockwise propagation. These transitions are mediated by transient standing-wave states and are accompanied by characteristic spectral sidebands indicating periodic alternation. Numerical integration and bifurcation analysis using AUTO suggest that alternation may arise from periodic dwelling near coexisting saddle-node bifurcation points, with the alternation frequency following a square-root scaling law with respect to heterogeneity strength. This mechanism highlights a deterministic route to symmetry selection in nonlinear media, providing a minimal model relevant to alternation phenomena in plasma, fluid, and biological systems. This system, thus, serves a minimal platform for studying symmetry-reselection transitions in extended nonlinear media.