Binary-oscillator networks: Bridging a gap between experimental and abstract modeling of neural networks

This paper proposes a simplified oscillator model, called binary-oscillator, and develops a class of neural network models having binary-oscillators as basic units. The binary-oscillator has a binary dynamic variable upsilon = +/-1 modeling the ''membrane potential'' of a neuron, and due to the presence of a ''slow current'' (as in a classical relaxation-oscillator) it can oscillate between two states. The purpose of the simplification is to enable abstract algorithmic study on the dynamics of oscillator networks. A binary-oscillator network is formally analogous to a system of stochastic binary spins (atomic magnets) in statistical mechanics.