Univ. of Illinois, Urbana-Champaign

Prof. Mark Nelson

1. In this problem you will simulate
conductance changes at a single
synapse, in response to a train of uniformly spaced input spikes. The
conductance
change is described by:
The impulse response is the alpha function: Write a MATLAB program that uses the two first-order differential equations to simulate conductance changes in response to a train of uniformly spaced input spikes. Model the spike input as: (a) Simulate the following four cases and turn
in plots of conductance
vs. time.
Your output should look similar to the
following graph. |

EXTRA CREDIT: (b) Demonstrate mathematically that the two first-order differential equations are equivalent to the single second-order differential equation at the top of the page. (c) Demonstrate mathematically that the peak of the alpha function occurs when t = tau. (HINT: show that the first derivative goes to zero and that the second derivative is negative at that point.) |