Mathematical model about the relationship between two animal species
The model you present here is a special case of the Lotka-Volterra competition equations, where the two species have the same effect on each other (i.e., symmetric competition). Some things to think about in interpreting this:


each species has a negative effect on the other (i.e., increasing the density of either species lowers the other's population growth rate), hence this is a "negative-negative" interaction; it makes more sense for two species that are competing with each other (for resources, space, enemy-free space, etc ...) than for a predator-prey system such as the shark-whale example you give. 
In contrast, in predator-prey (or more broadly "enemy-victim") systems, one species (the predator) benefits from the association - its population growth rate increases when the density of the other species (the prey) increases - and the other species (the prey) suffers (its population growth rate goes down when the predator density increases)
the fact that the competition is symmetric (this happens because you are using the sum of the population, $M+N$, and not using a competitive asymmetry parameter, e.g. $M+\alpha_{MN} N$) means that this would be most suited to modeling the competition between species that were very similar to each other (e.g. the same size, resource-gathering ability, etc.)