Chaotic Dynamics: Theory and Applications to Economics

ISBN-13: 9780521484619 / Angielski / Miękka / 1995 / 364 str.

Alfredo Medio; Alfredo Medio;Medio Gallo

Opis

This book is a tool for the theoretical and numerical investigation of nonlinear dynamical systems modelled by means of ordinary differential and difference equations. Special attention is given to the analysis and understanding of chaotic dynamics. The work is divided into two parts: a book, comprising a theoretical overview of the subject matter and a number of applications; and an integrated software program (called DMC) together with its manual.Although the emphasis is laid on dynamical systems arising from economic motivation, and the applications are derived from these systems, both the text and the program will also be of use to researchers in other fields of study. While it is not intended to be a textbook in mathematics, the mathematical language is of a precision comparable to that used in analogous books for applied scientists. The book first discusses the fundamental concepts and methods of chaos theory, and then applies these theoretical results and the facilities provided by the companion software program to models suggested by economic problems.The software program accompanying this book is available on disk in DOS and Macintosh formats. These can ba ordered using the order form contained in the book.

Spis treści

Preface; Part I. Theory: 1. General introduction: chaos and economics; 2. Basic mathematical concepts; 3. A user's guide; 4. Surfaces of sections and Poincaré maps; 5. Spectral analysis; 6. Lyapunov characteristic exponents; 7. Dimensions; 8. Symbolic dynamics; 9. Transition to chaos: theoretical predictive criteria; 10. Analysis of experimental signals: some theoretical problems; Part II. Applications to Economics: 11. Discrete and continuous chaos; 12. Cycles and chaos in overlapping generations models with production; 13. Chaos in a continuous-time model of inventory business cycles; 14. Analysis of experimental signals; Part III. Software: 15. DMC manual; 16. MODEL; 17. EVAL; 18. PLOT; 19. STAT; 20. FILES; 21. UTIL; 22. OPTS; 23. QUIT; 24. Internal menu commands; 25. DMC internal compiler.