Adaptive Synchronization of Nonlinear Neural Oscillator Networks Under Time-Delay Perturbations

Abstract

Nonlinear neural oscillator networks are widely used to describe rhythmic coordination and coherent timing in brain-inspired dynamical systems. Synchronization in these networks becomes more difficult under time-delay perturbations because delayed coupling can distort phase alignment, increase transient mismatch, and weaken collective stability. Recent studies have examined delayed synchronization and adaptive control in neural-network models, but robust adaptive synchronization under explicit time-delay perturbations remains less explored. This article develops an adaptive synchronization framework that combines delayed network dynamics, synchronization error modeling, adaptive gain regulation, and stability-oriented analysis. The results show that low-delay conditions support rapid convergence, whereas stronger delay produces larger transient error and slower recovery; however, the adaptive controller restores coherence by increasing control effort only when mismatch becomes significant. Overall, the study demonstrates that adaptive control provides a practical route for preserving stable collective dynamics in delayed nonlinear neural oscillator networks.