Create a script to calculate rabbit and fox populations based on test case $2.$ Case $1.$ Base rabbit$-$fox model. Influence

of initial conditions.

Case $2.$ Find initial conditions that

maintain steady population

levels.

Case $3.$ Rabbits limited by food supply.

Case $4.$ Adt a grouse population to the

model. Note on Case $2.$ Steady$-$state

response

Seek initial conditions for $r$

and $f$ that make the

derivatives dr$/$dt and df$/$dt

zero simultaneously.

$d\frac{r}{d}t=0=\{$right$-$hand$-$

side $1\}$

Hintidf$/$dt $dr={20}_p=$ sssibightshand$-$ one is

hisided antd finit $=0.$

we are not interested in this

solution.

Steady$-$State for Fox$-$Rabbit

Model

$0=GRR*rss-$EFR$*fss*rss$

$0=GRF*fss+ER{F}^{*}rs{s}^{*}fss$ Rabbit population is correct

Fox population is correct

rss is correct

fss is correct

Rabbit and fox population plots are correctly formatted

Plot the rabbit and fox populations on a single plot. Include plot formatting $($axis labels, legend$).$

Click the run button to test your code output using the provided script

Click the submit button to have your work assessed.

You have a $4$ submission limit$.$

Script $o.$

$\%$ Below are the parameters for your script.

$\%$ Try adjusting the parameters in MATLAB to see if the model behaves as you would predict. The parameters in MATLAB grader are locked.

GRR$=0\mathrm{.}4$; $\%$ Growth rate rabbit

EFR$=0\mathrm{.}032$; $\%$ Effect of fox on rabbit

GRF$=-1\mathrm{.}0$; $\%$ Growth rate fox

ERF$=0\mathrm{.}02$; $\%$ Effect of rabbit on fox

tinit$=0.$;

tfinal$=60.$;

delt$=0\mathrm{.}05$