How is this ODE created?

Question

So what I got was this but it doesn't match the answer sheet so not sure what went wrong

Answer 1

It's the line "with carrying capacity proportional to the population of the fish". You also mix up the two variables $N$ and $F$.

The system looks like this: \begin{align} \frac{dN}{dt} &= r_N N\left(1 - \frac{N}{cF}\right),\\ \frac{dF}{dt} &= r_F F\left(1 - \frac{F}{K}\right) - \alpha FN. \end{align}

Answer 2

In general, any model can be described as follow

dX/dt=gain-loss

the first term in equation 1 the gain is rf

and the loss is the second term.The brakes term () is called the logistic growth.

k in the equation reprints carrying capacity.In other words it can control how the variable is increasing or decreasing.

When k is large the fraction is small and vice versa.

the second equation.

in general think of it like this

+ve term is usually growth and -ve term is the loss.

P.s.

this model usually called predator-prey or lot Volterra.

good luck