Laboratoire d'informatique de l'École polytechnique

Talk by Antonio Jiménez-Pastor: « Exact nonlinear reductions of dynamical systems »

Speaker: Antonio Jiménez-Pastor
Location: Grace Hopper Meeting Room
Date: Tue, 28 Jun 2022, 11:00-12:00

The last meeting of the MAX team seminar for this semester will be on Tuesday, June 28.

Abstract: Dynamical systems of the form x’ = f(x) are widely used in many sciences. Numerical procedures, such as simulation and parameter estimation do not work efficiently due to the high dimension of the dynamical systems. We studied exact reductions of the system, i.e., computing macro-variables that satisfy self-consistent differential systems. Thanks to the software CLUE, we can reduce the dimension of polynomial and rational dynamical systems by a linear change of variables (i.e., macro-variables are linear combinations of the original variables) preserving some linear quantities from the original state variables. In this talk we are going to present a new method to reduce the dimension of these dynamical systems even further by performing a nonlinear change of variables. We are going to show how to look for reductions of this type, how to preserve some information from the original system and how to compute the new self-consistent system that the new macro-variables satisfy.