Complex Systems

My first contact with the field of complex systems was the implementation of a stochastic version of Greenberg-Hasting dynamics on a Small-World Network. The purpose was to study the collective extinct-active transition of the network under the stochastic modification of the Greenberg-Hasting dynamics. Even more, it was studying the activity of two interconnected networks with just one or two links between them. This project was presented at the SIAM Workshop on Network Science 2018 (NS18) [1].

Disease dynamics is one of the most difficult fields in complex systems, from my perspective, due to the number of degrees of freedom. However, that doesn't mean that the field is not exciting. During my undergraduate, I implement a toy model for the spreading of mosquitoes based on Voronoi diagrams. The key idea was to model the transmission dynamics of dengue between mosquitoes and humans. However, due to the lack of time the project ended just in the model of the spreading dynamics of the mosquitoes. The model uses the Voronoi diagrams and its dual, which correspond to the Delaunay graph to obtain the geometric and topological information of a city. The generators of the diagrams are the sites of standing water, where the mosquito can start to reproduce. The discrete dynamics were characterized by three states: black infected zone, red susceptible to become infected by the mosquitoes, and green clean zone. Once, a zone is infected by the mosquitoes, it is run a discrete version of the logistic equation that models the reproduction of the mosquitoes. When the population of mosquitoes reaches a maximum that is proportional to the area of the infected zone, the mosquitoes with certain probability travel to one of the adjacent susceptible zones. Then, it was applied two controls to dynamics: one to prevent susceptible zones, and another for clean infected zones [6]. This project was presented in the Sixth International Conference on Analytic Number Theory and Spatial Tessellations. The project was supposed to be published in the proceedings of the conference; however, due to some inconvenience with the organization and some servers the paper was not published.