Problem $2$: Two Species Model

$\frac{dx}{dt}=0\mathrm{.}7x(1-\frac{x}{10})-y$

$\frac{dy}{dt}=0\mathrm{.}8y(1-\frac{y}{8})+xy$

$2\mathrm{.}1$ Create a Simulink model of the system and recreate the given plots.

$2\mathrm{.}2$ Run the above model from a MATLAB file and create a single XY graph of all the solutions

starting at $5$ different sets of initial states.

$2\mathrm{.}3$ Use MATLAB "trim" and "linmod" commands to find the equilibrium points of the original

model $($above$)$ and analyze their stability.

$2\mathrm{.}4$ Will the model behave differently if the interaction term of the prey's equation changes from

$"-$y$"$ to $"-$xy$".$ Explain, re$-$calculate and simulate $($just for one nonzero initial state$).$