Re: Izhikevich neuron has no stable state

The Izhikevich model can capture lots of different types of neuron behavior, including behavior where it simply bursts and spikes spontaneously (like real neurons do).   Check out this site:

http://vesicle.nsi.edu/users/izhikevich/publications/whichmod.htm#izhikevich

If you have matlab then the script on that site (which I just discovered today) is a nice way to get a feel for the model.  I've attached a small network file (for Simbrain v. 2; see the bottom of this post) that has the parameter values for the "integrator," which I am guessing is something like the integrate and fire model.  It stays in a stable state absent input but it increases its rate of firing as the value of the neuron on the left is increased (just select it and press the up button).

The matlab script at Izhikevich's site has a nice summary of parameter values for different types of neural behaviors:

A            B        C      D       I (Input from other neurons)
0.02      0.2     -65      6       14 % tonic spiking
0.02      0.25    -65      6       0.5  % phasic spiking
0.02      0.2     -50      2       15 % tonic bursting
0.02      0.25    -55     0.05     0.6 % phasic bursting
0.02      0.2     -55     4        10  % mixed mode
0.01      0.2     -65     8        30  % spike frequency adaptation
0.02      -0.1    -55     6        0   % Class 1
0.2       0.26    -65     0        0   % Class 2
0.02      0.2     -65     6        7   % spike latency
0.05      0.26    -60     0        0   % subthreshold oscillations
0.1       0.26    -60     -1       0   % resonator
0.02      -0.1    -55     6        0   % integrator
0.03      0.25    -60     4        0   % rebound spike
0.03      0.25    -52     0        0   % rebound burst
0.03      0.25    -60     4        0   % threshold variability
1         1.5     -60     0      -65   % bistability
1       0.2     -60     -21      0   % DAP
0.02      1       -55     4         0   % accomodation
-0.02      -1      -60     8        80  % inhibition-induced spiking
-0.026     -1      -45     0        80 % inhibition-induced bursting

It should be fun to try these out (just open the neuron property dialog for an Izhikevich neuron and enter appropriate values.  For I values it's a little more complicated and I can explain if you ask; but most of them are 0 anyway).   I'll include this list in the next version of the documentation.

Now, since you asked about this, I'll point out that I implemented the Izhikevich neuron quickly and without any optimization, and I never really tested it.  So I'd love it if you or anyone in the open  source community could validate (or even optimize!) the behavior of Simbrain's implementation of the Izhikevich model.  As I noted in another post on this forum just now, I only have time to work on this in my spare time so not everything works perfectly...

All best,

- Jeff

izhik_test.net