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Dynamical Systems Theory

  • Oscar Castillo
  • Patricia Melin
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 63)

Abstract

This chapter introduces the basic concepts of dynamical systems theory, and several basic mathematical methods for controlling chaos. The main goal of this chapter is to provide an introduction to and a summary to the theory of dynamical systems with particular emphasis on fractal theory, chaos theory, and chaos control. We first define what is meant by a dynamical system, then we define an attractor, and the concept of the fractal dimension of a geometrical object. Also, we define the Lyapunov exponents as a measure of the chaotic behavior of a dynamical system. On the other hand, the fractal dimension can be used to classify geometrical objects because it measures the complexity of an object. We finish the chapter by reviewing mathematical methods for controlling chaos in dynamic systems. These methods can be used to control a real dynamic system, however, due to efficiency and accuracy requirement we will be forced to consider more advanced methods in the following chapters.

Keywords

Fractal Dimension Periodic Orbit Lyapunov Exponent Chaotic System Chaotic Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Physica-Verlag Heidelberg 2001

Authors and Affiliations

  • Oscar Castillo
    • 1
  • Patricia Melin
    • 1
  1. 1.Department of Computer ScienceTijuana Institute of TechnologyChula VistaUSA

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