8. Conclusions

In previous sections, we have stablished a pattern of dynamic behavior for 2-D maps, which have been used to model ecological systems. The dynamic pattern allows to state that for any 2-D maps that shows chaotic dynamics for a set of parameters, we can always find two of such parameters that, when alternate, yield a periodic trajectory. This conjecture is an extension of the so-called Parrondo's paradox, in the sense that two undesirable dynamics can be alternate to yield a desirable dynamics. In other words, we can always find a region in parameter space, where we can select a pair of such parameters. Therefore, we the developed methodology can be use, in general, as a chaos control approach, and, in particular, we can use it to model, in the case of ecological maps, seasonality. Although we interested in ecological relevant 2-D maps, we believed that our conjecture can be extended to other type of 1-D and 2-D maps. Finally, we consider that the major application of the methodology is in controlling chaotic dynamics.

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