Delay asymmetry induces a functional separation between sensitivity and coordination

Delayed interactions are ubiquitous in physical, biological, and engineered systems, yet delay is typically treated as a single parameter governing stability or synchronization. Here we demonstrate that delayed nonlinear systems generically exhibit a functional separation between sensitivity to delay asymmetry and coordination between interacting units. Using a minimal stochastic delayed system, we systematically varied delay asymmetry and quantified sensitivity via Fisher information and coordination using an information–phase composite index. We find that sensitivity to asymmetry emerges immediately upon symmetry breaking and peaks at very small normalized delay differences (Δτ/T₀ ≈ 0.07–0.08). In contrast, coordination develops more slowly and reaches its maximum at substantially larger asymmetries (Δτ/T₀ ≈ 0.30). No single delay configuration simultaneously optimizes both objectives. Mode-wise analysis reveals that this separation originates from a redistribution of information from collective to differential modes as asymmetry increases. Crucially, this phenomenon is absent in phase-only delayed Kuramoto models, indicating that delay geometry alone is insufficient. Instead, amplitude dynamics and amplitude–phase coupling are essential. Validation using delayed Stuart–Landau oscillators confirms that shear (non-isochronicity) amplifies early sensitivity by converting noise-driven amplitude fluctuations into phase information. Together, these results establish delay asymmetry as a functional resource, revealing a fundamental dynamical principle by which systems balance responsiveness and coordinated structure without fine-tuning to criticality.