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

  • Gian Italo Bischi
  • Anastasiia Panchuk
  • Davide Radi
Conference proceedings

Part of the Springer Proceedings in Complexity book series (SPCOM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Gian Italo Bischi, Fabio Lamantia, Davide Radi
    Pages 1-159
  3. Ingrid Kubin, Pasquale Commendatore, Iryna Sushko
    Pages 213-256
  4. Fabio Lamantia, Davide Radi, Lucia Sbragia
    Pages 257-289
  5. Back Matter
    Pages 325-327

About these proceedings


The book presents the lectures delivered during a short course held at Urbino University in summer 2015 on qualitative theory of dynamical systems, included in the activities of the COST Action IS1104 “The EU in the new economic complex geography: models, tools and policy evaluation”. It provides a basic introduction to dynamical systems and optimal control both in continuous and discrete time, as well as some numerical methods and applications in economic modelling.

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.


COST Action IS1104 Complex Economic Geography Complex Economic Systems Continuous-time Dynamical Systems Discrete-time Dynamical Systems Decision-driven Evolving Systems Dynamical Systems and Optimal Control Economic Dynamics Event-driven Evolving Systems Geocomplexity Proceedings Nonlinear Socioeconomic Dynamics Regional and Spatial Economics

Editors and affiliations

  • Gian Italo Bischi
    • 1
  • Anastasiia Panchuk
    • 2
  • Davide Radi
    • 3
  1. 1.Università di Urbino "Carlo Bo"UrbinoItaly
  2. 2.National Academy of Sciences of UkraineKiewUkraine
  3. 3.LIUC - Università CattaneoCastellanzaItaly

Bibliographic information