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A recent review of Lorenz's model [99] [100] progression spanning from 1960 to 2008 revealed his adeptness at employing varied physical systems to illustrate chaotic phenomena. These systems encompassed Quasi-geostrophic systems, the Conservative Vorticity Equation, the Rayleigh-Bénard Convection Equations, and the Shallow Water Equations.
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. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal.
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In the OGY method, small, wisely chosen, kicks are applied to the system once per cycle, to maintain it near the desired unstable periodic orbit. [3] To start, one obtains information about the chaotic system by analyzing a slice of the chaotic attractor. This slice is a Poincaré section. After the information about the section has been ...
Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory. [8] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set ...
Chaotic scattering is a branch of chaos theory dealing with scattering systems displaying a strong sensitivity to initial conditions. In a classical scattering system there will be one or more impact parameters , b , in which a particle is sent into the scatterer.
Looking at the entire chaotic domain, whether it is chaotic or windowed, the maximum and minimum values on the vertical axis of the orbital diagram (the upper and lower limits of the attractor) are limited to a certain range. As shown in equation (2-1), the maximum value of the logistic map is given by r/4, which is the upper limit of the ...