Standard Article

Catastrophe Theory

  1. Robert Gilmore

Published Online: 15 JUL 2007

DOI: 10.1002/3527600434.eap052.pub2

Encyclopedia of Applied Physics

Encyclopedia of Applied Physics

How to Cite

Gilmore, R. 2007. Catastrophe Theory. Encyclopedia of Applied Physics. .

Author Information

  1. Drexel University, Department of Physics and Atmospheric Science, Philadelphia, Pennsylvania, U.S.A.

Publication History

  1. Published Online: 15 JUL 2007

Abstract

The article contains sections titled:

  • 1
    Introduction
  • 2
    What It Is
    • 2.1
      The Program of Catastrophe Theory
    • 2.2
      Three Theorems from Elementary Calculus
      • 2.2.1
        Implicit Function Theorem
      • 2.2.2
        Morse Lemma
      • 2.2.3
        Thom Splitting Lemma
    • 2.3
      Thom Classification Theorem
    • 2.4
      Thom's List of Elementary Catastrophes
    • 2.5
      Why a List of Perturbations is Required
    • 2.6
      Geometry of the Fold and the Cusp
      • 2.6.1
        Geometry of the Fold Catastrophe
      • 2.6.2
        Geometry of the Cusp Catastrophe
      • 2.6.3
        Bifurcation Sets for the Three-Dimensional Catastrophes
    • 2.7
      Perturbations of Gradient Dynamical Systems
  • 3
    Why It Exists
    • 3.1
      A Simple Example
    • 3.2
      General Procedure
    • 3.3
      A More Complicated Example
  • 4
    How It Works
    • 4.1
      Catastrophe Conventions
    • 4.2
      Catastrophe Flags
      • 4.2.1
        Modality
      • 4.2.2
        Sudden Jumps
      • 4.2.3
        Inaccessibility
      • 4.2.4
        Sensitivity
      • 4.2.5
        Hysteresis
      • 4.2.6
        Divergence of Linear Response
      • 4.2.7
        Time Dilation (Critical Slowing Down, Mode Softening)
      • 4.2.8
        Anomalous Variance
    • 4.3
      The Dangers of Design Optimization
    • 4.4
      Elementary Catastrophes in Nonlinear Dynamics
  • 5
    Appendix: A Brief History of Catastrophe Theory