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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 ...
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 ...
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.
The Origins of Chaos Theory. While Lorenz might be known for coining the “Butterfly Effect” in relation to chaos theory, Lin says that the discovery of chaos theory actually dates back to the ...
Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics. The figure shows the main ideas running in each direction. Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory.
These subregions are called bands . When there are multiple bands, the orbit moves through each band in a regular order, but the values within each band are irregular . Such chaotic orbits are called band chaos or periodic chaos, and chaos with k bands is called k -band chaos . Two-band chaos lies in the range 3.590 < r < 3.675, approximately .
These monographs include an idea of Poincaré, which later became the basis for mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems. Poincaré authored important works on astronomy for the equilibrium figures of a gravitating rotating fluid.
In that context, he developed the Gutzwiller trace formula, the main result of periodic orbit theory, which gives a recipe for computing spectra from periodic orbits of a system. He is the author of the classic monograph on the subject, Chaos in Classical and Quantum Mechanics (1990).