L'=L(nS-d) where
- b is the birth rate of small fish
- d is the death rate of large fish
- e is the chance of a small fish being eaten (per large fish and time unit)
- n is analogous to the nutritional value of small fish eaten (by one large fish) in unit time
What happens when a species becomes too dominant for its own good is very clearly shown at the left (or lower) part of the graph above. The equations are well-conditioned and any second order method will be enough. The improved Euler method is not much of a program, so the site has added automatic scaling of axes, automatic determination of the simulation time step and the total duration of the simulation to make it slightly more interesting.
The assumption of two species only is simplistic and there is a limit to how much even large fish can eat. Still, this looks a successful model for many conditions, even though it is almost 100 years old.
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