Learning to Oscillate: Hebbian Plasticity Imprints Limit Cycles in Neural Networks

A high-dimensional nonlinear recurrent neural network is driven by periodic, incoherent inputs while its synapses undergo Hebbian-like plasticity. Depending on drive and plasticity strengths, the network can retain autonomous limit-cycle activity after both the inputs and learning are removed. Dynamical mean-field theory and finite-size simulations characterize the resulting rhythmic memories and transitions between chaotic, fixed-point and oscillatory regimes. Memory robustness depends on the interval between removing the input and stopping plasticity. These results suggest a mechanism by which neural circuits learn and maintain biological rhythms.