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Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
Ralph Douglas Stacey (October 1948 – September 4 2021) was a British organizational theorist and Professor of Management at Hertfordshire Business School, University of Hertfordshire, in the UK and one of the pioneers of enquiring into the implications of the natural sciences of complexity for understanding human organisations and their management.
The nature of chaos theory suggests that the predictability of any system is limited because it is impossible to know all of the minutiae of a system at the present time. In principle, the deterministic systems that chaos theory attempts to analyze can be predicted, but uncertainty in a forecast increases exponentially with elapsed time. [2]
The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible [citation needed]. Computational irreducibility explains why many natural systems are hard to predict or simulate.
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators and cardiac tissues. [6] attempt the control of chaotic bubbling with the OGY method and using electrostatic potential as the primary control variable.
Butterfly effect image. The butterfly effect describes a phenomenon in chaos theory whereby a minor change in circumstances can cause a large change in outcome. The scientific concept is attributed to Edward Lorenz, a mathematician and meteorologist who used the metaphor to describe his research findings related to chaos theory and weather prediction, [1] [2] initially in a 1972 paper titled ...
Shaw was one of the pioneers of chaos theory and his work at University of California, Santa Cruz on the subject was among the first research into the relationship between predictable motion and chaos in a landmark PhD thesis. [3] He was part of the Dynamical Systems Collective with J. Doyne Farmer, Norman Packard, and James Crutchfield. The ...