I'm reading about mathematical models of biological neural networks, which can be grouped into two categories:
The model accounts for the fact that a signal takes time to travel from the excitatory to excited neuron
The signal is modeled as if it travels instantaneously between neurons
I'm trying to understand whether a signal delay is introduced for the purpose of realistically modelling a neural network, or whether it has other functional roles in the model. So by function I mean a role in the information-processing capacity of the network that extends mere physical limitations of axon signaling. I'm referring specifically to their function in biological neural networks
Here are three distinct cases that I expect the answer should fall under, to further illustrate what I mean by function:
They don't, signal delays are a mere physical necessity of biological neural networks, irrelevant for the information-processing aspect of their operation. The differences between delay durations are primarily due to the fact that low reaction times are metabolically expensive and spatially-inefficient and are thus reserved for specialized purposes such as reflexes, instead of having a wider functional role as a parameter.
They do, signal delays are fundamentally required for neural networks to process spatio-temporal patterns. However, the differences between the durations of delays are unnecessary to explain any fundamental internal property and are still due to external factors.
They do, and the differing durations themselves are operational parameters, i.e. the function of a sub-network can only be fully understood if the ratios of the delays in signal transfers are taken into account.