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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
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]
During the first systemic phase of his work he applied first chaos theory and then the models of complex adaptive systems to organisations and management arguing that organisations are complex adaptive systems and that the patterns in the actions of organisations, which are their strategies, emerge unpredictably in self organising processes ...
In particular the theory of random graphs has been used as a justification for self-organization as a general principle of complex systems. In the field of multi-agent systems , understanding how to engineer systems that are capable of presenting self-organized behavior is an active research area. [ 45 ]
The perturbation must be tiny compared to the overall size of the attractor of the system to avoid significant modification of the system's natural dynamics. [2] Several techniques have been devised for chaos control, but most are developments of two basic approaches: the Ott–Grebogi–Yorke (OGY) method and Pyragas continuous control. Both ...
Chaos theory is sometimes pointed out as a contradiction to Laplace's demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. [9]
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 ...
By comparison, based on the concept of attractor coexistence within the generalized Lorenz model [26] and the original Lorenz model ([36] [37]), Shen and his co-authors [35] [38] proposed a revised view that “weather possesses both chaos and order with distinct predictability”. The revised view, which is a build-up of the conventional view ...