Exercise $2\mathrm{.}8$

a$.$ Use MATLAB to produce a phase plane of the system $(14)$ above, with the parameter values $a=3,b=1,c=2,d=3.$ Set the minimum values of $x$ and $y$ to $-1$ and the maximum values to $10.$ Where in the $x-y$ plane are the physically possible solutions? $($Remember$,x$ and $y$ represent populations. Can they become negative?$)$

b$.$ On your phase plane, use drawphase to plot three solution curves in the first quadrant from time zero to time $25.($i$.$e$.,$ tmax$=25.)$ Note that because of rounding error, dr awphase might fail to close a loop exactly. Include the graph in your Word document.

c$.$ The predator$-$prey system has the following states:

A$.$ The populations of foxes and rabbits are both relatively small.

B$.$ The small number of foxes allows the rabbit population to increase.

C$.$ The increased number of rabbits allows the number of foxes to increase.

D$.$ The decreased supply of rabbits causes the fox population to decrease, returning to state $A.$

On your plot in your Word document, mark one of the solutions $($that is$,$ one loop$)$ with the states $A,B,C,$ and $D$ at the locations where they occur on that solution.

Please provide the code for A and B$!$