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Once Pecora asked himself whether chaos could be useful. playful physicist with a ….. May I have the phone number for Colonel Y?” “I cannot confirm or deny that anyone … “I cannot confirm or deny that he works here. isn’t it?
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Cuomo’s method relies on this synchronized chaos, a somewhat mysterious discovery summarized in a 1990 paper [2] by Louis Pecora and Thomas Carroll at The Naval Research Laboratory. The phenomenon occurs in some situations when part of the outputof one chaotic system is used as an input for a twin chaotic system. If the two systems are properly synchronized, then the second system will mimic the behavior of the first with uncanny fidelity.
Just like Pecora, Carroll, Cuomo, and Oppenheim have done, we’ll look at synchronization in the chaotic Lorenz system (look at my post Edward Lorenz’s Strange Attraction for a Deeper Dive into the Lorenz system). The system comes from Edward Lorenz’s simplification of an atmospheric convection model, and its intriguing chaotic behavior has been studied for decades. It is defined by the following system of nonlinear differential equations:
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http://logicaltightrope.com/2013/09/01/sending-your-secrets-safely-with-chaos/
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A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called arepeller (or repellor).
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But are we sure of our observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one’s observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory.Sir Arthur Stanley Eddington (1882-1944) English astronomer and physicist.
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Butterfly effect creator!