# 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 ?
Zheng, "Adaptive robust fuzzy control for a class of uncertain chaotic systems," Nonlinear dynamics, vol.
Liu, "Parameter estimation for chaotic systems by particle swarm optimization," Chaos, Solitons and Fractals, vol.
Chaotic systems present highly sensitive to initial conditions; that is, they present different chaotic dynamics when the initial conditions are slightly modified.
Adaptive H8 synchronization of unified chaotic systems.
The sensitivity to initial conditions means predicting the behaviour of a chaotic system is difficult, and becomes more difficult over time.
15) Hence, it is possible to consider chaotic systems as generating rather than destroying order, insofar as a random scattering of initial points in the phase space will end up being in a more ordered rather than less ordered state as they converge on the attractor.
Chaotic systems have been proven to be having correlation with cryptography [2].
The inherent property of robustness of a Fuzzy Logic System (FLS) makes it an efficient forecaster for chaotic systems.
Since the seminal work by Carroll Pecora [1,2], a variety of impressive approaches have been proposed for the synchronization for the chaotic systems such as PC method [1,2], sampled-data feedback synchronization method [4], OGY method [5], adaptive design method [6,7], time-delay feedback approach [8], backstepping design method [9,10], sliding mode control method [11], active control method [12], etc.
This means that the two Lorenz chaotic systems realize the projective synchronization under the controller (10).
According to that, many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems [3].
In other calculations, the researchers found that with some basic tweaks in the design, the new class of metamaterials could also model chaotic systems, such as disordered planetary motions, by inducing chaos in electromagnetic waves.
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