In many fishery science models, the speed at which a fish is caught is assumed to be directly proportional to its abundance. If both the predator and the prey are being exploited in this way, modify the Lotka-Volterra model to consider this case.
Solution
Let $x$ be the number of specie $x$ at time $t$, $y$ be the number of predators of specie $x$ at time $t$ and $c$ be the number of caught of specie $x$ at time $t$.
Then $$\frac{dc}{dt}=ax$$ $$\frac{dx}{dt}=-lxc-mxy+ax$$ $$\frac{dy}{dt}=-lyc+dxy-by$$
Did I represent the system correctly according to the text presented here? If not, could you help me to correct it?
Could anyone check it, please?
Thanks in advance.
Why is $dc/dt = ax$? $ax$ represents the rate of increase of the prey species in the absence of predators or fishing. There's no reason for this to be the rate at which these fish are caught. Also the terms $-lxc$ and $-lyc$ are wrong.