Aufgabe 6: Synchrony of two I&F Neurons

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 rates
^{1}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.

- A well suited measure for the quality of synchronization is the
cross-correlation
^{2}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 in
`sync.m`and which are important to reproduce your results.

- ... rates
^{1} - The vectors
`st1`and`st2`contain all firing times of neuons 1 and 2. - ... PSCs
^{2} - The PSCs are available in the vectors
`psc1`and`psc2`.