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NONLINEAR DYNAMICS AND CHAOS PART I: A GEOMETRICAL APPROACH

Published online by Cambridge University Press:  01 December 1998

Alfredo Medio
Alfredo Medio
Affiliation:
University “Ca' Foscari” of Venice
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Abstract

This paper is the first part of a two-part survey reviewing some basic concepts and methods of the modern theory of dynamical systems. The survey is introduced by a preliminary discussion of the relevance of nonlinear dynamics and chaos for economics. We then discuss the dynamic behavior of nonlinear systems of difference and differential equations such as those commonly employed in the analysis of economically motivated models. Part I of the survey focuses on the geometrical properties of orbits. In particular, we discuss the notion of attractor and the different types of attractors generated by discrete- and continuous-time dynamical systems, such as fixed and periodic points, limit cycles, quasiperiodic and chaotic attractors. The notions of (noninteger) fractal dimension and Lyapunov characteristic exponent also are explained, as well as the main routes to chaos.

Keywords

Nonlinear DynamicsAttractorCyclesChaosFractal DimensionLyapunov Exponents
Type
MD SURVEY
Information
Macroeconomic Dynamics , Volume 2 , Issue 4 , December 1998 , pp. 505 - 532
Copyright
© 1998 Cambridge University Press

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