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The Lorenz equations can arise in simplified models for lasers, [4] dynamos, [5] thermosyphons, [6] brushless DC motors, [7] electric circuits, [8] chemical reactions [9] and forward osmosis. [10] Interestingly, the same Lorenz equations were also derived in 1963 by Sauermann and Haken [11] for a single-mode laser.
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]
Lorenz was born in 1917 in West Hartford, Connecticut. [5] He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at the Massachusetts Institute of Technology, and his maternal grandfather, Lewis M. Norton, developed the first course in chemical engineering at MIT in 1888.
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 ...
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 Malkus waterwheel, also referred to as the Lorenz waterwheel or chaotic waterwheel, [1] is a mechanical model that exhibits chaotic dynamics. Its motion is governed by the Lorenz equations. While classical waterwheels rotate in one direction at a constant speed, the Malkus waterwheel exhibits chaotic motion where its rotation will speed up ...
However, equation (3-11) is a 16th-order equation, and even if we factor out the four solutions for the fixed points and the 2-periodic points, it is still a 12th-order equation. Therefore, it is no longer possible to solve this equation to obtain an explicit function of a that represents the values of the 4-periodic points in the same way as ...
It is the Lorenz attractor, that is to say, the one corresponding to the original differential equations, and its geometric structure that interest them. Pomeau and Ibanez combine their numerical calculations with the results of mathematical analysis, based on the use of Poincaré sections.