Qualitative theory for nonautonomous dynamical systems and applications (R-5173)

This project aims at developing the qualitative theory of nonautonomous (time-dependent, random or control) systems in new directions beyond the traditional setting that are highly relevant in applied sciences, but almost unexplored. The central aim of this research project is to develop insights and tools in random qualitative theory and multi-scale dynamical systems from a mathematical viewpoint which have a potentially high impact on applied sciences. In this context, it is particularly challenging to detect the simplest form of a system under a smoothness equivalence relation. This leads to new insights in the almost unexplored field of nonautonomous bifurcation theory. The proposal aims at making significant progress to develop the qualitative theory of nonautonomous dynamical systems in three main directions: Smooth linearization theory for nonautonomous differential equations, Smooth linearization for random dynamical systems and Smooth normal form theory for slow-fast systems. This development will be applied to predict the bifurcation or critical point in complex systems which are used as models of a lot of phenomena in life.

Keywords:DYNAMICAL SYSTEMS

Disciplines:Mathematical sciences and statistics