Nonlinear Dynamical Systems in Economics - Lines, Marji; SpringerLink (Online service) (Vienna : Springer Vienna : Imprint: Springer, 2005)
Many problems in theoretical economics are mathematically formalized as dynam ical systems of difference and differential equations. In recent years a truly open approach to studying the dynamical behavior of these models has begun to make its way into the mainstream. That is, economists formulate their hypotheses and study the dynamics of the resulting models rather than formulating the dynamics and studying hypotheses that could lead to models with such dynamics. This is a great progress over using linear models, or using nonlinear models with a linear approach, or even squeezing economic models into well-studied nonlinear systems from other fields. There are today a number of economic journals open to publishing this type of work and some of these have become important. There are several societies which have annual meetings on the subject and participation at these has been growing at a good rate. And of course there are methods and techniques avail able to a more general audience, as well as a greater availability of software for numerical and graphical analysis that makes this type of research even more excit ing. The lecturers for the Advanced School on Nonlinear Dynamical Systems in Economics, who represent a wide selection of the research areas to which the the ory has been applied, agree on the importance of simulations and computer-based analysis. The School emphasized computer applications of models and methods, and all contributors ran computer lab sessions.
Introductory Notes on the Dynamics of Linear and Linearized Systems -- Complex and Chaotic Dynamics in Economics -- Ergodic Theory of Nonlinear Dynamics -- Local Bifurcation Theory Applied to OLG Models -- Heterogeneous Agent Models: two simple examples -- Complex Oligopoly Dynamics -- Coexisting Attractors and Complex Basins in Discrete-time Economic Models.
Keywords: Economic theory; Economic growth; Macroeconomics; Economic Theory/Quantitative Economics/Mathematical Methods; Economic Growth; Macroeconomics/Monetary Economics//Financial Economics