Superexcitability in Chiral Oscillators with Spatial Degrees of Freedom

This work presents a numerical investigation of interacting chiral oscillators (COs), characterized by an intrinsic rotational handedness. The coupling of positional and orientational degrees of freedom drives a mutual influence between synchronization and spatial dynamics. The control parameter, Δ (anisotropy or detuning), represents the frequency difference between two COs (for the two-body case) or between two families of COs (for the many-body case) with opposite handedness. For two COs with opposite handedness, interaction forces generate a Helical Excitable Dipole (HED), where excitability is a spatiotemporal act characterized by a helical trajectory. For many COs moving in 2Ds, the model displays a locking-to-unlocking transition of the Kuramoto kind driven by Δ, and, within the locking region, many "superexcitable" states sustained by a global saddle-node bifurcation, detected by the collective period behavior versus Δ. These coherent, topological states are characterized by dissipationless phase-momentum locking, which I quantified using appropriate global metrics, including the Kuramoto order parameter and the novel parameter S capable of detecting the phase-momentum locking. These states exhibit a wide variety of topologically protected vortex complexes, whose complexity increases with system size. The model provides a unified framework for diverse biophysical applications—from molecular ratchets to cardiac looping—identifying the symmetry breaking of motile excitable units as a fundamental process for large-scale, robust collective transport.