fLIF

Almost all of my neural simulations have been based on fatiguing Leaky Integrate and Fire Neurons.
It's a pretty good model of biological neural behaviour, but is also pretty fast to simulate.
There is a lot of work being done by others with Leaky Integrate and Fire Neurons.
What neurons do is collect activation from other neurons that have connections to them. That's Integrate.
If a neuron collects enough activation (surpassing a threshold), it fires sending activation to neurons that it is connected to. (IF)
If a neuron fires it loses all its activity.
If it doesn't fire, some of the activity leaks away. (LIF)
I simulate in discrete cycles so activity at t is activity at t-1 divided by a leak factor.
I'm not familiar with many people simulating fatigue in neurons.
The idea is that a neuron gets tired.
I typically model this with a fatigue constant that raises the activation threshold when a neuron fires. It's reduced if the neuron doesn't fire.
Neurons are inhibitory or excitatory but not both.
Topology. Uni-directional sparse connections.
I typically use distance-biased connectivity but have used random connectivity more recently to get a hold of the math.

Fatiguing Leaky Integrate and Fire Neurons