Introduction to Chaotic Dynamical Systems

Abstract

The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1992
Accession Number
ADA261747

Entities

People

  • Michael A. Bernhard

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Autonomous Systems
  • Calculus
  • Differential Equations
  • Dynamics
  • Eigenvalues
  • Equations
  • Linear Systems
  • Mathematics
  • Nonlinear Dynamics
  • Nonlinear Systems
  • Notation
  • Numbers
  • Phase Diagrams
  • Social Sciences
  • Two Dimensional

Readers

  • Control Systems Engineering.
  • Research Science/Academic Research
  • Systems Analysis and Design