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Chaos theory has applications in a variety of disciplines, including meteorology, [9] anthropology, [16] sociology, environmental science, computer science, engineering, economics, ecology, and pandemic crisis management.
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then ...
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 ...
Chaotic cryptology is the application of mathematical chaos theory to the practice of cryptography, the study or techniques used to privately and securely transmit information with the presence of a third-party or adversary. Since first being investigated by Robert Matthews in 1989, [1] the use of chaos in cryptography has attracted much ...
As a pedagogic tool, the Malkus waterwheel became a paradigmatic realization of a chaotic system, and is widely used in the teaching of chaos theory. [3] In addition to its pedagogic use, the Malkus waterwheel has been actively studied by researchers in dynamical systems and chaos. [4] [5] [6] [7]
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.
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 book approaches the history of chaos theory chronologically, starting with Edward Norton Lorenz and the butterfly effect, through Mitchell Feigenbaum, and ending with more modern applications. The book covers chaos theory under the lens of four themes: sensitive dependence on initial conditions, self-similarity, universality, and ...