Universal Evolutionary Model for Periodical Species

Figure 7

Attractors for tuples and from Proposition 4. Both tuples generate predator-prey interaction, with the species being the prey. For , does not depend on (it may feed on other items), but has to escape; hence, global fixed points are those with . For there is dependence between the prey and the predator: the species must eat in order to survive, and must escape from in order to survive. Local fixed points are those with prime and (cicadas-like behavior). Here, also , so the species disappears.