Chaos Theory

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Chaos Theory

A theory stating that seemingly unrelated events affect each other in a predictable, mathematical way. In investing, chaos theory is used to predict future stock prices using information that does not seem to affect prices directly, such as trading volume and trader sentiment. Computing these factors using chaos theory is as complex as it is controversial.
References in periodicals archive ?
A Novel Image Encryption Scheme Based on Chaotic Maps.
This algorithm is the combination of the chaotic map and charge system search algorithm.
Kawamura, Chaotic maps on measure spaces and convergence of orbits of states Proc.
A new pseudo-random number generator based on two chaotic maps.
The selected chaotic map for all experiments is the Logistic map, whose equation is given in Eq.
Further, a one-way coupled chaotic map lattice was used by Huaping et al [43] for generating pseudo-random numbers.
Chaos search: In this algorithm, when a random number is needed by the classical DE algorithm, it is generated by iterating one step of the chosen chaotic map that has been started from a random initial condition at the first iteration.
There are three basic steps in the method of Fridrich [8]: (a) choose a chaotic map and generalize it by introducing some parameter, (b) discretize the chaotic map to a finite square lattice of points that represent pixels, (c) extend the discretized map to three-dimensions and further compose it with a simple diffusion mechanism.
This contrasts with the fact that, from the viewpoint of symbolic dynamics, chaotic maps are able to produce any symbol pattern, and for this reason they are used in practice to generate pseudo-random sequences.
13] Wen GL, Xu D, Observer-based control for full-state projective synchronization of a general class of chaotic maps in ant dimension.
Designed for a full year course for upper level undergraduates, this covers nonlinear and chaotic maps, time series analysis, autonomous systems in the plane, nonlinear Hamilton systems, nonlinear dissipative systems, nonlinear driven systems, controlling and synchronization of chaos, fractals, cellular automata, differential equations, neural networks, genetic algorithms, gene expression programming, optimization, discrete wavelets, discrete hidden Markov processes, and fuzzy sets with fuzzy logic.
This type of stretching and folding is characteristic of chaotic maps.