Database Schema for the Global Dynamics of Multiparameter Nonlinear Systems

Common features of models of multiscale phenomena include nonlinearities that are based on heuristic arguments, poorly measured, understood or controlled parameters, and imprecise experimental data.  With this in mind I will present a combinatorial/topological framework for classifying and describing the global dynamics of nonlinear systems over multidimensional parameter spaces. These methods allow for a priori assumptions on the imprecision of measurements in phase space and parameter space. The results are a representation of the dynamics in the form of a queryable database from which one can obtain coarse, but mathematically rigorous, descriptions of the dynamics over large ranges of nonlinearities and parameter values.