Glossary of Complexity Theory


  • Artificial neural network (ANN)
    * Complex dynamical system in which the nodes are analogs of biological neurons, and the connections are arranged so that the whole system performs as an analog of a biological nervous system.
  • Attractor
    * Dynamical equilibrium of a DS
    * Attracts all nearby points
    * Three types: static (point), periodic (cyclic), chaotic
  • Basin of attraction
    * Most important attribute of an attractor of a DS
    * Set of initial points tending to the same attractor
  • Bifurcation
    * Change in the attractor/basin portrait of a dynamical scheme
    * Characterized by a loss of stability
    * Three types: subtle, explosive, and catastrophic
  • Catastrophe theory
    * Branch of math created by Rene Thom ca 1966
    * Study of catastrophic bifurcations of a dynamical scheme
  • Cellular automaton, CA
    * Type of math model created by John von Neumann ca 1952
    * A lattice of identical finite state machines interconnected by a rule, the same at each node
    * Exm: Conway's Game of Life
  • Cellular dynamaton, CD
    * aka cellular dynamical system, or lattice dynamical system
    * Type of math model due to Rashevsky ca 1930
    * Discrete model for partial differential equations of evolution type
  • Chaos theory
    * Synonym for dynamical systems theory
  • Complex dynamical systems theory
    * Synonym for chaos theory
  • Complexity
    * Measure of complexity of a dynamical system or one of its attractors.
  • Complexity theory
    * Study of complex dynamical systems
    * Especially, schemes of cellular dynamical systems
  • Cybernetics
    * Field created by Norbert Wiener ca 1942
    * Diffused by the Macy Conference, 1946
    * Wiener's book publ 1948
  • Dynamical scheme
    * Family of DS depending on control parameters
  • Dynamical system, DS
    * Two types: continuous, discrete
  • Dynamical system, continuous
    * Autonomous system of ordinary differential equations
  • Dynamical system, discrete
    * Iterated map system, iterated function system
  • Dynamical systems theory, DST
    * Branch of math founded by Poincare ca 1882
    * Early roots in Lord Rayleigh's work on musical instruments
    * Qualitative (or geometric) theory of dynamical systems
  • General Evolution Theory, GET
    * Offshoot of GST and SD due to Ervin Laszlo ca 1985
    * Developed by the General Evolution Research Group, GERG
  • General Systems Theory, GST
    * Field created by Von Bertalanffy ca 1950
    * Study of properties shared by all complex systems
  • Gestalt theory
    * Holistic branch of psychology due to Wertheimer, Kohler
    * Berlin ca 1930
    * Applied to social theory by Kurt Lewin, founder of social psych
  • Emergence
    * Roughly equivalent to self-organization
    * Study of emergence of order in a field of chaos
    * Appearence of a property or simplicity in a CDS scheme
    * Study of bifurcations in a cellular dynamical scheme
    * Related to morphogenesis
  • Homeokinetics
    * Field founded by Arthur Iberall ca 1950
    * General theory of evolution in physical, biological, and social systems
  • Homeostasis
    * Term introduced by W. B. Cannon ca 1932 or perhaps Claude Bernard ca 1850
    * Stable equilibrium of a natural system
    * Same as static (point) attractor in DST
  • Homeorhesis
    * Term introduced by C. H. Waddington ca 1957
    * Dynamic equilibrium of a natural system
    * Non-static attractor of a DS
  • Morphogenesis
    * Branch of math founded by Alan Turing ca 1952 with ancient and classical roots, eg, Kepler, Goethe.
  • Politicometrics
    * Application of DST to wars and arms races
    * Created by Lewis Frye Richardson ca 1920
  • Self-organization
    * Synonym for emergence
  • System dynamics, SD
    * Applied version of DST
    * Founded by Jay Forrester ca 1950
    * Applied to the world system in the Limits to Growth study sponsored by the Club of Rome
  • Theoretical biology
    * Mythical field similar to theoretical physics
    * Search for laws applying to all biological systems
    * Waddington's Serbelloni conferences, 1966, 1967, 1968, 1970

  • Revised 27 May 2002 by Ralph Abraham, <abraham@vismath.org>