Differential Equations, Stability and Chaos in Dynamic Economics

This is the first economics work of its kind offering the economist the opportunity to acquire new and important analytical tools. It introduces the reader to three advanced mathematical methods by presenting both their theoretical bases and their applications to a wide range of economic models.

The mathematical methods presented are ordinary differential equations, stability techniques and chaotic dynamics. Topics such as existence, continuation of solutions, uniqueness, dependence on initial data and parameters, linear systems, stability of linear systems, two dimensional phase analysis, local and global stability, the stability manifold, stability of optimal control and empirical tests for chaotic dynamics are covered and their use in economic theory is illustrated in numerous applications. These applications include microeconomic dynamics, investment theory, macroeconomic policies, capital theory, business cycles, financial economics and many others.

All chapters conclude with two sections on miscellaneous applications and exercises and further remarks and references. In total the reader will find a valuable guide to over 500 selected references that use differential equations, stability analysis and chaotic dynamics. Graduate students in economics with a special interest in economic theory, economic researchers and applied mathematicians will all benefit from this volume.

This book will be of immense value to mathematical economists, economic theorists and to many mathematicians; it is to be strongly recommended.
The Economic Journal
H.-W. Lorenz
The large number of topics treated in the text and the precision and clarity of the exposition make it probable that this book will be referred to as a standard reference in economic dynamics in the years to come.
Mathematical Reviews
M. Boldrin
....a superb book that I highly recommend to theoretical and applied economists alike............it will become a classic reference tool for anybody using continuous-time, dynamical methods in economics.
Journal of Political Economy