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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 ...
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 ...
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.
“Chaos is a fact of life … and a part of dynamical systems theory,” Lin explains to Popular Mechanics in an email. “Some systems are inherently chaotic, while others are not.
Chaos: Making a New Science is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public. [1] It was a finalist for the National Book Award [ 2 ] and the Pulitzer Prize [ 3 ] in 1987, and was shortlisted for the Science Book Prize in 1989. [ 4 ]
In this book, Stewart explains chaos theory to an audience presumably unfamiliar with it. As the book progresses the writing changes from simple explanations of chaos theory to in-depth, rigorous mathematical study. Stewart covers mathematical concepts such as differential equations, resonance, nonlinear dynamics, and probability. The book is ...
Dynamical systems and chaos theory state that at least 3 degrees of freedom are necessary for a dynamic system to be chaotic. Three-dimensional flows have three degrees of freedom corresponding to the three coordinates, and usually result in chaotic advection, except when the flow has symmetries that reduce the number of degrees of freedom. In ...
Balance of nature – superseded by catastrophe theory and chaos theory. Progression of atomic theory. Democritus, the originator of atomic theory, held that everything is composed of atoms that are indestructible. His claim that atoms are indestructible is not the reason it is superseded—as it was later scientists who identified the concept ...