Cascade process and Pareto rule: application to runoff data of two Mexican rivers (Conchos and Nazas)

摘要

This paper has two objectives: the first is to show that the annual runoff of rivers such as Conchos and Nazas (Mexico), follow the Pareto rule of 80:20 when classes are ordered from largest to less, and can be compared with cascade processes. The second objective is to show that cascade process produce the core which gives rise to fractional integral and therefore to differential equations of fractional order. Finally, we conclude that the Pareto rule is a first approach to saturation described by the complementary characteristic function, and runoff data provide the order of the temporal derivative. Therefore, cascade processes are manifested ubiquitously in nature, and show us a way to evolve towards the imbalanced and become in distribution mechanisms that turn into a transition that destroys old and build new correlations.