For a ring with 5 neurons:
10 neurons:
25 neurons:
As you can see, while the behavior is pretty much the same between a network with 5 and 10 neurons, where the spike just sort of oscillates around the network, with each neuron activating the next, by the time I got to a network with 25 neurons, the same current injection didn't end up exciting any neurons except the one that the current was directly injected into. Any guess why this behavior is cropping up? Since each neuron in my model is identical, I don't know why the size of the overall network should matter; wouldn't the fact that each neuron is only connected to two identical neurons mean the same behavior should occur in all 3 models, but that the amount of time between spikes for the same neuron should be larger as the network grows larger?