Question $1$: Give a discussion of the parameter sensitivity of the Neural Transmitter

Model, by multiplying Alfa $(),$ Beta $(),$ Gama $()$ and I$0(I_0)$ with $10,5,2,1,0\mathrm{.}5,0\mathrm{.}2$

and $0\mathrm{.}1,$ respectively. The default values are: Alfa$=2$;$=5$;Gama$=0\mathrm{.}5$; and $I0=1.$ Then

comment on the role of each parameter.

Steps:

$(1)$ Play with the attached program in Matlab by multiplying parameters with $10,5,2,1,$

$0\mathrm{.}5,0\mathrm{.}2$ and $0\mathrm{.}1,$ plot out the responses in ONE figure for each parameter, e$.$g$.,$ with $7$

different Alfa values and all other parameters in default values.

$(2)$ Similarly, find the relationship between the overshoot $($calculate use the formula

given in class, do not measure it from figure$)$ and parameters, respectively. Plot

figures of overshoot v$.$s$.$ each parameter.

$(3)$ Similarly, find the relationship between the time constant and parameters,

respectively. Plot figures of time constant v$.$s$.$ each parameter.

$(4)$ The program and the model dynamics for the default case are in the Appendix $1.$