Qualitative Theory of Dynamical Systems, Tools and Applications for Economic Modelling
Lectures Given at the COST Training School on New Economic Complex Geography at Urbino, Italy, 17-19 September 2015
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Economic and social systems are intrinsically dynamic, characterized by interdependence, nonlinearity and complexity, and these features can only be approached using 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 though 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 to describe event-driven (often decision-driven) evolving systems.
The book is written for Ph.D. and master's students, post-doctoral fellows, and researchers in economics or sociology, and it only assumes a basic knowledge of calculus. However it also suggests some more advanced topics.