## 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
- Artificial neural network (ANN)
Revised 27 May 2002 by Ralph Abraham, <abraham@vismath.org> |