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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 ...
Folded-towel map attractor. A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents. [1]Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent.
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 ...
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.
First experimental confirmation of self-excited chaos from Chua's circuit was reported in 1985 at the Electronics Research Lab at U.C. Berkeley. [13] First confirmation of hidden chaos was reported in 2022 at the Theoretical Nonlinear Dynamics Lab at the Institute of Radio-engineering and Electronics of the Russian Academy of Sciences. [5] [14]
In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracles.It represents the idea of creating a universal scheme with modular design and customizable parameters, which can be applied wherever randomness and sensitiveness is needed.
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 ...
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 ...