title: Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory.
abstract: We study pulse-coupled neural networks that satisfy only two assumptions: each isolated neuron fires 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 oscillatory associative memory, or what minimal adjustments should be made so that it can acquire memory. In the search for such minimal adjustments we obtain a large class of simple pulse-coupled neural networks that can memorize and reproduce synchronized temporal patterns the same way a Hopfield network does with static patterns. The learning occurs via modification of synaptic weights and/or synaptic transmission delays.
authors.affiliation: Center for Systems Science and Engineering, Arizona State University, Tempe, AZ 85287-7606, USA.
authors.forename: E M
authors.initials: EM
authors.lastname: Izhikevich