Weakly Pulse - Coupled Oscillators , FM Interactions , Synchronization , and Oscillatory

| We study pulse-coupled neural networks that satisfy only two assumptions: each isolated neuron res periodically, and the neurons are weakly connected. Each such network can be transformed by a piece-wise continuous change of variables into a phase model, whose synchronization behavior and oscillatory associative properties are easier to analyze and understand. Using the phase model, we can predict whether a given pulse-coupled network has os-cillatory associative memory, or what minimal adjustments should be made so that it acquires the memory. In search for such minimal adjustments we discover a large class of simple pulse-coupled neural networks that can memorize and reproduce synchronized temporal patterns the same way a Hoppeld network does static patterns. The learning occurs via modiication of synaptic weights and/or synaptic transmission delays.