Modeling izhikevich neurons

Support
1

Description of problem

Hi everybody , i try to model three neuroun Izhekivch with two astrosyte ,but i don’t know how model the synaps_eqs in brian2 please help me and here is my equations but i don’t know is true or not :
#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

2

Hi Maryidea,

section 2.4 Astrocytes of Modeling neuron–glia interactions with the Brian 2 simulator might be especially useful to you. [code for figure]

-Adam

3

Hi adam ,

thank you for your help , i read Modeling neuron–glia interactions with the Brian 2 simulator but my problem is in implementation of izhikevich neuron , may i have your email and send you the article and i explain my problem?

4

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.

2 Likes
5

thank you so much, i try to do it