Periodic and Chaotic Events in a Discrete Model of Logistic Type for the   Competitive Interaction of Two Species
  Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. This work, together with two other similar ones recently published by the authors, completes a triptych dedicated to the two-species relationships present in Nature, namely the symbiosis, the predator-prey and the competition. These models can be used as basic ingredients to build up more complex interactions in the ecological networks. 
Ricardo Lopez-Ruiz and Daniele Fournier-Prunaret