ABSTRACT
Both terrestrial and aquatic ecosystems are networks involving interactions among living beings and their environment. The reductionist approach brings us to isolate interactions between pairs of elements. A recurrent type of simplified interaction in ecosystems is that involving one kind of predator and one kind of prey. Lotka and Volterra proposed the simplest model to describe the predator-prey interaction. Their model admits a limit cycle as a stable solution. More sophisticated models are also described. They differ in the type of functional response describing how the predator consumes prey. Whatever is the model, there is a spontaneous tendency to observe oscillations in the number of predators and prey, in agreement with experimental evidence. In any ecosystem, there are many more symbiotic relationships. They are all treated with the same general chemical kinetic mechanism. The only difference is in the stoichiometric coefficients. Apart from the predator-prey fight, the other symbiotic relationships do not exhibit oscillations in time.
