Problem $1$: Logistic with Predation model

$5$

$0\mathrm{.}8(1)$

$203$

dy y y

y

dt y

$=$

$+$

$1\mathrm{.}1$ Create an EXCEL phase$-$plane plot of the given model.

$1\mathrm{.}2$ Create a Simulink model of the system. Run it for a few representative initial populations.

$1\mathrm{.}3$ Slightly modify the predation saturation and$/$or activation parameters $($without making any of

them zero or negative$)$ for the model to become logistic without extinction $($not necessarily the

original logistic model $$ another logistic model$).$ Show the EXCEL plot and a Simulink

verification.

$1\mathrm{.}4$ Slightly modify the predation saturation and$/$or activation parameters $($without making any of

them zero or negative$)$ for the model to become global extinction $($that is$,$ an extinction for any

initial population$).$ Show the EXCEL plot and a Simulink verification.Problem $1$: Logistic with Predation model

$\frac{dy}{dt}=0\mathrm{.}8y(1-\frac{y}{20})-\frac{5y}{3+y}$

$1\mathrm{.}1$ Create an EXCEL phase$-$plane plot of the given model.

$1\mathrm{.}2$ Create a Simulink model of the system. Run it for a few representative initial populations.

$1\mathrm{.}3$ Slightly modify the predation saturation and$/$or activation parameters $($without making any of

them zero or negative$)$ for the model to become logistic without extinction $($not necessarily the

original logistic model $-$ another logistic model$).$ Show the EXCEL plot and a Simulink

verification.

$1\mathrm{.}4$ Slightly modify the predation saturation and$/$or activation parameters $($without making any of

them zero or negative$)$ for the model to become global extinction $($that is$,$ an extinction for any

initial population$).$ Show the EXCEL plot and a Simulink verification.