Write systems of differential equations describing the above situation. Feel free to make up parameter values as needed.
1. Two predators that must eat each other to survive.
2. Two predators that must eat each other to survive, but with per capita production of each reduced by competition with its own species.
3. Two competitors where the per capita production of a is decreased by the total population, and the total population of b is decreased by the population of b.
4. Two competitors where the per capita production of each type is affected only by the population size of the other type.