Topology-Dependent Persistence of Synchronization in Noisy Coupled Oscillator Networks: A Modified Decay Law and Falsifiable Prediction

Coupled oscillator networks under additive noise are expected to exhibit exponential decay of the synchronization order parameter and convergence to an incoherent state beyond a characteristic noise-limited time scale. Numerical studies have explored topology-dependent synchronization persistence in structured networks. We propose a minimal phenomenological recurrence for local phase coherence on the oscillator graph that reproduces standard exponential desynchronization in unstructured networks but predicts delayed desynchronization and the emergence of a nonzero synchronization plateau when repeated local motifs are present. The model is parameterized by a single topology-dependent memory strength α(μ) and yields closed-form expressions for the order parameter r(d) with a calculable plateau height and build-up time scale. Matched-pair network simulations (identical node count, coupling strength, and noise level, differing only in motif density) provide a direct falsification protocol. If no separation is observed, the model is ruled out; if plateaus emerge as predicted, it offers a new diagnostic for topology-induced memory in noisy coupled dynamical systems.