I'm starting work on a computational neuroscience project where I want to create my own model of a spiking Hodgkin-Huxley neuron and connect many instances (about 400) of this model through synapses. Is there a generally accepted way to do this? I have experience in Python and Matlab but I'm wondering if there are any good packages or other software to create neurons and connecting them into a network?
I am old and my experience with this area is 20 years out of date, but I would still go with https://neuron.yale.edu/neuron/
You can simulate a network of hodgkin huxley neurons quite easily with Brian, a python package for simulating networks of neurons. http://briansimulator.org/demo/ <- there's actually a demo of what you want here, I think.
There is also Neuron, as a previous poster answered, but I don't think you need this unless you are doing morphologically detailed simulations.