Ring of Neurons with Delayed Connections

The animations below show the oscillation patterns that can occur in a ring of neurons with timed delayed connections between the neurons. In each case, all neurons are oscillating with the same frequency, all that changes is the phase differences between the neurons and the amplitudes of the oscillations.

For an odd number of neurons there are 4 possible patterns.

Synchronized oscillation. All neurons have the same phase. All amplitudes are the same.
Travelling wave. Nearest neighbours are 1/nth of a period out of phase, where $n$ is the number of neurons. All amplitudes are the same
Mirror reflecting wave. Amplitudes of in phase neurons are the same.
Standing wave. Amplitudes of anti-phase neurons are the same.

For an even number of neurons two patterns are stable.

Synchronized oscillation. All neurons have the same phase. All amplitudes are the same.
Antiphase oscillation. Nearest neighbours are half a period out of phase. All amplitudes are the same.

All animations were prepared using XPPAUT.

Here is the pdf file of a talk relating to these animations.