Discretization and Solvency Algorithm for the Dynamics of Multistates of a Continuum System
Graphs, State Spaces, Diffusion process, Modelling, SIR Model.
Given the uncertainty in which real systems operate, especially when it involves, by its nature, unpredictable human actions or machine malfunctions. It becomes necessary to search for determinı́stic models, which contribute to the understanding of the dynamic behavior of a system, at the basic level. Such systems can be described by probabilı́stic models, taking advantage of certain features of regularity that they exhibit. Thus, one can resort to Stochastic Processes as a way to treat these phenomena quantitatively, depending on certain characteristics one can resort to Markov Processes. Given a dynamical system, whose dynamics can be given in continuous or discrete time, a study of its evolution of states over time is necessary. In some applications, the distinction between continuous and discrete systems is not critical, and the choice is made for convenience. This work seeks the description of an algorithm that is able to discretize the system studied, in a natural way, thus forming a connected graph, in order to study the dynamics of states of this same graph over time. Thus, given the input, it can generate the appropriate output, thus answering the questions pertinent to the system.