Interplay of coupling and forcing: Coherence in a nonlinear delayed oscillator

Abstract

Coupled oscillators often experience two distinct influences: an internal input transmitted through coupling from a driver subsystem, and an external periodic forcing applied directly to the response. Here we ask how these two influences interact and whether their combined action can organize the response dynamics. We show that coupling and forcing can cooperate to produce a localized organization in parameter space, where the response displays simultaneously enhanced steady-state amplitudes and increased spectral concentration at the forcing frequency; we term this effect coupling-forcing induced coherence. In delay regimes where the driver approaches a steady state, the coupling acts as an effective bias that shifts the response operating point, providing a resonance-like mechanism that helps anchor the onset of the coherent band. When the driver is also externally forced, coupling-forcing induced coherence can coexist with transmitted resonance (amplification conveyed from the driver to the response through the coupling pathway). We use frequency- and time-domain diagnostics to identify parameter regions dominated by coupling-forcing induced coherence, by transmitted resonance, or by their combined action.