synchronization .. synchronized chaos ..

Mastering Chaos

"The method devised by Ott, Grebogi and Yorke (referred to as OGY ) is conceptually straightforward. To start, one obtains information about the chaotic system by analyzing a slice of the chaotic attractor. After the information about this so-called PoincarĂ© section has been gathered, one allows the system to run and waits until it comes near a desired periodic orbit in the section. Next the system is encouraged to remain on that orbit by perturbing the appropriate parameter. One strength of this method is that it does not require a detailed model of the chaotic system but only some information about the PoincarĂ© section. It is for this reason that the method has been so successful in controlling a wide variety of chaotic systems."

"Whereas some investigators have searched for uses of chaos, others have sought to control it. One key to this effort lies in the realization that a chaotic attractor is an infinite collection of unstable periodic behaviors."

"If several identical systems whose attractors are all period two or greater are driven by the appropriate pseudoperiodic signal, they will all get in step."

.. they will get ..in step .. what does it bring to mind .. lock-stepped Bose-Einstein condensates ..

"Until this discovery, scientists had no reason to believe that the stability of a subsystem could be independent of the stability of the rest of the system. Nor had anyone thought that a nonlinear system could be stable when driven with a chaotic signal."

nonlinear system .. be stable .. nonlinear taken out by virtue --- of the many processes involved each one following its own trajectory .. the meeting place .. where they exchange ..information about the states they are in .. states out of .. the input-outcome procedures .. each process is involved in .. the notion of synchronization enters as .. the jump of the system to the next stage .. to state out of all the outcomes of the meeting processes .. the arrangements of the outcome states .. outcome states which contribute to the values of variables measured .. observed in the system .. the displayed as apparent complexity ..

synchronization that brings into mind .. tuning .. melody .. music .. what makes the chords vibrate .. vibrate in unison .. in fact, when I write these lines .. synchronization is at bay .. it is the result of synchronized processes ..that grapple with words and their meanings .. as they instantiate in my mind ..

"Stability depends not only on the properties of the subsystem itself but on the driving signal. A subsystem may be stable when driven by one type of chaotic signal but not when driven by another. The trick is to find those subsystems that react to a chaotic signal in a stable way. In some cases, the stability of a subsystem can be estimated using a mathematical model, but in general such predictions are difficult."

"Stability depends not only on the properties of the subsystem itself but on the driving signal."

the implications of that thought .. stability .. ingrained within .. the much sought-after order ..

stability .. or otherwise order .. in a system .. depend not only on the properties of the system\subsystem .. but on the driving signal .. the very driving signal employed to synchronize chaotic systems .. to attain stability .. hence order ..

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