Pasquale Commendatore "Introducing COST Action IS1104: The EU in the new complex geography of economic systems: models, tools and policy evaluation”

The qualitative theory of dynamical systems, started by Poincaré on the early XX century and developed along the Fifties and Sixties by the Russian School of Andronov, in the last 40 years has been more and more applied to the description of the time evolution of economical and social systems. These systems are intrinsically dynamic, characterized by interdependence, nonlinearity and complexity. These featured can only be approached by a qualitative analysis, based on the study of invariant sets (equilibrium points, limit cycles and more complex attractors, together with the boundaries of their basins of attraction) which requires a trade-off between analytical, geometrical and numerical methods. Even if the early steps of the qualitative theory of dynamical systems have been in continuous time models, in economic and social modelling discrete time is often used, in order to describe event-driven (often decision-driven) evolving systems. In this three-days training school a basic introduction to the qualitative theory of dynamical systems will be given, both in continuous and discrete time, and some applications in economic and social problems, as well as some numerical tools, will be proposed. The lectures will be at an elementary level, only assuming a basic knowledge of calculus. However some indications and suggestions about more advanced topics will be given.