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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."
This textbook on the theory of nonlinear dynamical systems for nonmathematical advanced undergraduate or graduate students is also a reference book for researchers in the physical and social sciences. It provides a comprehensive introduction including linear systems, stability theory of nonlinear systems, bifurcation theory, chaotic dynamics. Discussion of the measure--theoretic approach to dynamical systems and the relation between deterministic systems and stochastic processes is featured. There are a hundred exercises and an associated website provides a software program, computer exercises and answers to selected book exercises.
This textbook on the theory of nonlinear dynamical systems for nonmathematical advanced undergraduate or graduate students is also a reference book for researchers in the physical and social sciences. It provides a comprehensive introduction including linear systems, stability theory of nonlinear systems, bifurcation theory, chaotic dynamics. Discussion of the measure--theoretic approach to dynamical systems and the relation between deterministic systems and stochastic processes is featured. There are a hundred exercises and an associated website provides a software program, computer exercises and answers to selected book exercises.
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