Rhythmic Gating of Hebbian Plasticity in a Modified Wilson–Cowan Model as a Mechanism for Stability–Plasticity Balance

The Wilson-Cowan model is a set of two differential equations simulating the dynamics of interacting populations of excitatory and inhibitory neurons. In its original state, the model is applicable to epilepsy, however, this study seeks to (1) provide a template of the model capable of depicting brain function in learning, and effectively, memory; and (2) identify factors that are important for aiding learning processes in individuals diagnosed with learning disorders. A modified Wilson-Cowan model is introduced where synaptic weights evolve through Hebbian plasticity rules, incorporating weight decay to prevent runaway dynamics and a rhythmic modulation term to simulate gamma oscillations. Stability analysis of the unforced system reveals a single, asymptotically stable fixed point. When oscillatory modulation is applied, this fixed point evolves into a stable periodic orbit, demonstrating that plasticity is gated to specific phases of the gamma cycle, creating rhythmic "learning windows." This phase-dependent learning provides a mechanistic framework to the stability-plasticity dilemma by structuring synaptic modification in time, preventing chaotic growth while allowing continuous learning. The findings suggest that disruptions to this rhythmic organization may underlie learning deficits, and propose that interventions aimed at entraining brain oscillations could enhance learning by restoring optimal timing for synaptic plasticity.