# Aufgabe 6: Synchrony of two I&F Neurons

[10+3* Punkte, ausgegeben am 04.05.2005, Abgabe bis 24.05.2005, pdf, ps.gz]

The action potentials of two coupled I&F neuons may synchronize. In this exercise, you will examine the circumstances under which two coupled I&F neuons synchronise.

The Matlab program sync.m simulates two I&F neuons which are mutally coupled by two synapses. It plots the temporal evolution of the membrane potential, the spikes and the PSCs. You need to unzip the file csim.zip into the same directory as sync.m to make sync.m work. (it contains csim.dll for Windows and csim.mexglx for Linux).

1)
Do a simulation with the standard parameters. Describe / explain the result. At which rates1 do the neurons fire?

2)
Do a simultaion with I1=I2=18. I1 resp. I2 are external currents , which are injected into the neurons. Describe the results. Why do the neurons not synchronize?

3)
Do a simultaion with I1=I2=18, w = 30 resp. w=10. Describe the results. Describe the mechanism that leads to synchronization.

4)
Do a simultaion with w=30, Tsim=5.0, I1=18 and I2=18.5 respectively I2=22. Tsim defines the duration of the simulation. Describe / explain the results.

5)
Make some diagrams (think about well suited diagrams) which show quantitatively how the quality and speed of synchrony depends on which parameters. Describe / explain your approach and the results.

6*)
Examine how the results change if you add noise to the model (set the parameter Inoise ). Describe / explain the results.

### Notes

• A well suited measure for the quality of synchronization is the cross-correlation

between the PSCs2 and , where and are the averages of and over and are the considered time interval.

• You can use the time until is above a certain value (for a well suited choice of ) as a measure for the speed of synchronization.

• Present your results clearly arranged and document them in a way that one can reproduce then anytime.
• Return a printout ot the Matlab-Code not included insync.m and which are important to reproduce your results.

#### Fußnoten

... rates1
The vectors st1 and st2 contain all firing times of neuons 1 and 2.
... PSCs2
The PSCs are available in the vectors psc1 and psc2.

Neuronale Netzwerke B (SS05), Rober Legenstein, 2005