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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.
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.
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