Args:

prey$\_$initial $($float$)$: Initial prey value.

predator$\_$initial $($float$)$: Initial predator value.

params $($dict$)$: Parameters for the Lotka$-$Volterra system and simulation settings.

n$\_$steps $($int$)$: Number of time steps to simulate.

Returns:

numpy.ndarray: Array of prey and predator values over time $(2$ x n$\_$steps$).$

t$\_$span $=(0,$ params$["$delta t$"]**$ n$\_$steps$)$

t$\_$eval $=$ np$.$linspace$($t$\_$span$[0],$ t$\_$span$[1],$ n$\_$steps$)$

y $[$prey$\_$initial, predator$\_$initial$]$

sol $=$ solve$\_$ivp$($lambda t$,$ y: compute$\_$prey$\_$rate$($t$,$ y$,$ params$),$ t$\_$span, y$0,$ t$\_$eval$=$t$\_$eval, rtol$=1$e$-8,$ atol$=1$e$-8)$

return sol.y

prey$\_$initial $=0\mathrm{.}0$

predator$\_$initial $=10\mathrm{.}0$

params

"delta t$"$: $0\mathrm{.}001,$

"Prey reproduce": $0\mathrm{.}5,$

"Prey eaten": $0\mathrm{.}05,$

"Predator loss": $0\mathrm{.}015,$

"Predator reproduce": $0\mathrm{.}001,$

$"$n time steps": $100$

$\}$

n$\_$steps $=$ params$["$n time steps"$]$ # Retrieve the number of time steps from params. I run this code through the code block new$\_$populations$\_$check $=$ calculate$\_$n$\_$time$\_$steps$($prey$\_$initial, predator$\_$initial, params, n$\_$steps$)$

Can I please get help on this. I want to get to those values its asking for but I have to guess and check to get there. I don't think its the right way to go$.$