SO(2)-Networks as Neural Oscillators

Using discrete-time dynamics of a two neuron network with recurrent connectivity it is shown that for specific parameter configurations the output signals of neurons can be of almost sinusoidal shape. These networks live near the Sacker-Neimark bifurcation set, and are termed SO(2)-networks, because their weight matrices correspond to rotations in the plane. The discretized sinus-shaped waveform is due to the existence of quasi-periodic attractors. It is shown that the frequency of the oscillators can be controlled by only one parameter. Signals from the neurons have a phase shift of π/2 and may be useful for various kinds of applications; for instance controlling the gait of legged robots.