512 16 Bit Izhikevich Neuron

Izhikevich model 

The Izhikevich model is a simple spiking neuron model that builds on the 
    dynamics of the simplistic leaky integrate-and-fire model, adding 
    complexity of the Hodgkin-Huxley model with minimal computational 
    cost.

    The model is described by the following system:

        v' = 0.04*v^2 + 5*v + 140 - u + I
        u' = a*(b*v - u)
        if v >= 30 then {v = c; u = u + d}

        where: 
            a, b, c, d = dimensionless constants

                Regular Spiking (RS) Excitatory Neuron:
                    a = 0.02, b = 0.2, c = -65, d = 8

                
            v = membrane potential
            u = membrane recovery (Na and K, neg feedback to v)
            a = time scale of the recovery variable u (small = slow recovery)
            b = sensitivity of the recovery variable u to v
                    Larger values increase sensitivity and lead to more 
                    spiking behavior. b<a(b>a) is saddle-node
            c = after spike reset value of v
                    caused by fast K+ channels
            d = after spike reset value of u
                    caused by slow Na+ & K+ channels
            I = input current

    The constants for the model differential equation v' are experimentally
        determined by fitting the model to the desired neuron behavior. In 
        the original paper (from which the equations are taken), the model 
        was fit to experimental data from Regular Spiking of a rat cortical 
        neuron.


References:
https://www.izhikevich.org/publications/spikes.pdf

To test the model, use the supplied test-bench. The test-bench will run through
    three different scenarios. The first case is the reset test case, which 
    ensure that the model resets properly given a reset condition (res_n = 1).
    The next test case checks to make sure that the model doesn't spike when 
    the input current is below threshold. The spike value for each of these
    included non-spike test cases should be 0. The final test case is the spike 
    test that ensures the model spikes when the input is above the threshold. This
    includes a test for the maximum current to test overflow conditions. Each condition
    is checked with an assert statement.