So here’s an implementation for a single Izhikevich neuron (without synapses):

```
a = 0.02
b = 0.02
I = 0.0 # change this to increase the injected current
izhikevich_eqs = '''
dvm/dt = 0.04*vm**2 + 5*vm + 140 - u + I : 1
du/dt = a*(b*vm - u) : 1
'''
```

or the same version with units:

```
a = 0.02/ms
b = 0.2/ms
I = 0.0*volt/second
izhikevich_eqs = '''dvm/dt = (0.04/ms/mV)*vm**2+(5/ms)*vm+140*mV/ms-w + I : volt
du/dt = a*(b*vm-u) : volt/second
I : volt/second'''
```

page on izhikevich equations

brian documentation of basic izhikevich implementation

I’m happy to help, but I’d prefer to discuss here on the forum so others can help too, and so other people with the same question can see the solution.

i’ve reformatted the code you wrote so it’s easier for others to see here:

( you can get the same formatting on this forum by putting ``` before and after your code )

```
#neurone_astrocyte interaction model :
du_s/dt = (-u_s + tau_f*u_0*(1-u_s))/tau_f : 1
#directly and synaptically :
dx_s/dt = (1 - x_s - tau_dr_s ) /tau_d : 1
#indirectly and extra_synaptically:
dy_s/dt = (-y_s + tau_c * y_T*0.003*r_s) /tau_c : 1
synapses_action ='''
r_s = u_s * x_s
'''
```

Next I think it would be good to know a little more about the rest of your code (what variable names are you using for each neuron etc.) and what is and isn’t working.