A cyclic inhibitory network of three neurons oscillates for certain values of the parameters. The following movies show how the behaviour of the network changes as the value of the interneuron connections w is increased from -40 to 10. The other parameters such as biases, self-connections and time constants were fixed.

Neuron voltages shows how the time evolution of the voltages of the three neurons changes as the parameter w is varied. Notice that for very large negative values of the interneuron connection strength w the network approaches a steady state. When the value of w reaches -28 the network begins to oscillate until w reaches the upper limit -4, at which point the oscillations decay and the network again approaches a steady state.

Voltage correlation shows how the correlation between the voltages of neurons 1 and 2 changes as the parameter w changes. Also plotted is the graph of a target correlation, for which the network oscillates. Notice how the correlation changes as the network changes from trivial steady state to oscillatory behaviour and back to steady state. In the steady state case, the correlation is nearly constant. If the network is oscillating, the correlation oscillates as well.

Trace plot. The time-dependent voltages of the three neurons (V_1(t),V_2(t),V_3(t)) define a curve in Euclidean space called the trace. If the network approaches a steady state, this curve converges to the point in phase space representing the steady state. If the network oscillates, on the other hand, the trace approaches a limit cycle. Notice how the trace changes as the value of w changes from -50 to 10.

Shawn Lockery (Biology, University of Oregon) for his lectures, notes, ideas, and inspiration, on which this work is based.