Directional Bounded-Confidence Cucker-Smale Flocking

This research introduces a directional bounded-confidence extension of the Cucker-Smale (CS) flocking model. The approach decomposes pairwise relative velocities into radial and tangential channels within an instantaneous line-of-sight frame, utilizing compactly supported kernels to create state-dependent interactions. The authors establish an exact energy-dissipation identity with conserved mean velocity and prove exponential velocity consensus under a sliding-window persistent excitation condition. Additionally, a CS bounded-diameter criterion is derived to separate metric decay from aggregate directional coercivity. Simulations validate the dissipation balance and demonstrate that the proposed directional gating restores global alignment in scenarios where traditional isotropic confidence laws fail.