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Chaos theory 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. [1]
Edward Norton Lorenz. Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology. [1][2] He is best known as the founder of modern chaos theory, a ...
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.
A sample solution in the Lorenz attractor when ρ= 28, σ= 10, and β=83. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
Horseshoe map. In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator.
Sheila Scott Macintyre. Dame Mary Lucy Cartwright DBE FRS FRSE (17 December 1900 – 3 April 1998) [1] was a British mathematician. She was one of the pioneers of what would later become known as chaos theory. [2] Along with J. E. Littlewood, Cartwright saw many solutions to a problem which would later be seen as an example of the butterfly effect.
Logistic map. The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations.
This is a list of mathematical theories. Almgren–Pitts min-max theory; Approximation theory; ... Chaos theory; Character theory; Choquet theory; Class field theory;