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X-Y View of Lorenz Attractor 3. Chaos in Industry Since chaotic systems are systems that only appear to be random, but are really deterministic in nature, they possess an underlying order. This underlying order leads to the possibility of controlling chaotic systems.
William Ditto and Louis Pecora have been pioneering methods of controlling chaotic mechanical, electrical and biological systems . For example, Pecora and Thomas Carroll of the U. Naval Research Laboratory realized that synchronized chaos might be used for encoding private electronic communications.
An explanation of synchronized chaos is necessary here to understand what they did. Chaotic systems are described as having an infinite number of unstable periodic motions.
This instability means that no two chaotic systems can be built that provide the same output. However, it has been shown that if two identical stable systems are driven by the same chaotic signal, they will generate a chaotic output, but their inherent stability causes them to suppress differences between them.
The result is two identical chaotic outputs. At the sending location, generate a chaotic signal and use it as the input to a stable system to generate another chaotic output signal.
Mix the chaotic output signal with a message; the result is another signal that looks chaotic but has a message embedded in it. Now transmit two signals to the receiving location: At the receiving location, feed the original chaotic signal into a stable system identical to that at the sending location; the result is the same chaotic signal that was mixed with the message at the sending station.
Subtract this from the message-encoded chaotic signal and you have the original message. While it has been shown that it is not too difficult to intercept and extract the message from the chaos encoded message, if this method is layered on top of other encrypting methods, it enhances the security of private transmissions.
While the technique just discussed is a method of using chaos, others are working on methods of controlling chaos. Since a chaotic system is composed of an infinite number of unstable periodic orbits, the key to controlling the system is to wait until the system comes near the desired periodic orbit and then perturb the input parameters just enough to encourage the system to stay on that orbit.
Yorke who developed the system-has been used successfully in stabilizing lasers and other industrial systems. But the techniques employed in the OGY method are not limited to industry; they show promise in controlling chaotic behavior in the human body as well.
Chaos in the Human Body It has been argued that some cardiac arrhythmias are instances of chaos. This opens the doors to new strategies of control. The traditional method of controlling a system is to model it mathematically in sufficient detail to be able to control critical parameters.
However, this method fails in chaotic systems since no model can be developed for a system with an infinite number of unstable orbits.Fulfillment by Amazon (FBA) is a service we offer sellers that lets them store their products in Amazon's fulfillment centers, and we directly pack, ship, and provide customer service for these products.
reviews of Columbia Southern University written by students. The Foundation is a non-profit organization that seeks to promote essential change in education and society through the cultivation of fairminded critical thinking--thinking which embodies intellectual empathy, intellectual humility, intellectual perseverance, intellectual integrity and intellectual responsibility.
A sample reflective essay, written by a CI student. Below we offer an example of a thoughtful reflective essay that effectively and substantively capture the author's growth over time at California State University Channel Islands (CI).
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Carson McCullers (Author) Born in Columbus, Georgia, Carson McCullers was a prolific American writer of novels, short stories, essays, plays, and poetry.