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Over the last two decades there has been a great deal of research
into nonlinear dynamic models in economics, finance and the social
sciences. This book contains twenty papers that range over very
recent applications in these areas. Topics covered include
structural change and economic growth, disequilibrium dynamics and
economic policy as well as models with boundedly rational agents.
The book illustrates some of the most recent research tools in this
area and will be of interest to economists working in economic
dynamics and to mathematicians interested in seeing ideas from
nonlinear dynamics and complexity theory applied to the economic
sciences.
The materials in the book and on the accompanying disc are not
solely developed with only the researcher and professional in mind,
but also with consideration for the student: most of this material
has been class-tested by the authors. The book is packed with some
100 computer graphics to illustrate the material, and the CD-ROM
contains full-colour animations tied directly to the subject matter
of the book itself. The cross-platform CD also contains the program
ENDO, which enables users to create their own 2-D imagery with
X-Windows. Maple scripts are provided to allow readers to work
directly with the code from which the graphics in the book were
taken.
Over the last two decades there has been a great deal of research
into nonlinear dynamic models in economics, finance and the social
sciences. This book contains twenty papers that range over very
recent applications in these areas. Topics covered include
structural change and economic growth, disequilibrium dynamics and
economic policy as well as models with boundedly rational agents.
The book illustrates some of the most recent research tools in this
area and will be of interest to economists working in economic
dynamics and to mathematicians interested in seeing ideas from
nonlinear dynamics and complexity theory applied to the economic
sciences.
The investigation of dynamics of piecewise-smooth maps is both
intriguing from the mathematical point of view and important for
applications in various fields, ranging from mechanical and
electrical engineering up to financial markets. In this book, we
review the attracting and repelling invariant sets of continuous
and discontinuous one-dimensional piecewise-smooth maps. We
describe the bifurcations occurring in these maps (border collision
and degenerate bifurcations, as well as homoclinic bifurcations and
the related transformations of chaotic attractors) and survey the
basic scenarios and structures involving these bifurcations. In
particular, the bifurcation structures in the skew tent map and its
application as a border collision normal form are discussed. We
describe the period adding and incrementing bifurcation structures
in the domain of regular dynamics of a discontinuous
piecewise-linear map, and the related bandcount adding and
incrementing structures in the domain of robust chaos. Also, we
explain how these structures originate from particular
codimension-two bifurcation points which act as organizing centers.
In addition, we present the map replacement technique which
provides a powerful tool for the description of bifurcation
structures in piecewise-linear and other form of invariant maps to
a much further extent than the other approaches.
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