  If one isolated species is supposed to evolve following the logistic mapping,
then we are tempted to think that the dynamics of two species can be expressed
by a coupled system of two discrete logistic equations. As three basic
relationships between two species are present in Nature, namely symbiosis,
predator-prey and competition, three different models are obtained. Each model
is a cubic two-dimensional discrete logistic-type equation with its own
dynamical properties: stationarity, periodicity, quasi-periodicity and chaos.
Furthermore, these models could be considered as the basic ingredients to
construct more complex interactions in the ecological networks.
