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Nonlinear Dynamics And Chaos Part I: A Geometrical Approach

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  • Medio, Alfredo

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.

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  • Medio, Alfredo, 1998. "Nonlinear Dynamics And Chaos Part I: A Geometrical Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 2(4), pages 505-532, December.
    • Handle: RePEc:cup:macdyn:v:2:y:1998:i:04:p:505-532_00
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    Cited by:

    1. Joydeep Bhattacharya & Helle Bunzel, 2003. "Dynamics of the planning solution in the discrete-time textbook model of labor market search and matching," Economics Bulletin, AccessEcon, vol. 5(19), pages 1-10.
    2. Bhattacharya, J. & Bunzel, H., 2003. "Chaotic Planning Solutions in the Textbook Model of Labor Market Search and Matching," Discussion Paper 2003-15, Tilburg University, Center for Economic Research.
    3. Guo, Jang-Ting & Lansing, Kevin J., 2002. "Fiscal Policy, Increasing Returns, And Endogenous Fluctuations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 633-664, November.
    4. Bhattacharya, Joydeep & Bunzel, Helle, 2003. "Dynamics of the Planning Solution in the Discrete-Time Textbook Model of Labor Market Search and Matching," Staff General Research Papers Archive 10253, Iowa State University, Department of Economics.
    5. Bhattacharya, J. & Bunzel, H., 2003. "Chaotic Planning Solutions in the Textbook Model of Labor Market Search and Matching," Other publications TiSEM da7233db-ec71-41f8-b3d6-d, Tilburg University, School of Economics and Management.

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