Controlling Chaos: Theoretical and Practical Methods in - download pdf or read online
By Tomasz Kapitaniak
Greater than 20 years of extensive reports on non-linear dynamics have raised questions about the sensible functions of chaos. One attainable resolution is to manage chaotic habit in a predictable means. This ebook, oneof the 1st at the topic, explores the information in the back of controlling chaos.
Controlling Chaos explains, utilizing basic examples, either the mathematical conception and experimental effects used to use chaotic dynamics to actual engineering structures. Chuas circuit is used for instance through the booklet because it might be simply built within the laboratory and numerically modeled. using this instance permits readers to check the theories offered. The textual content is punctiliously balanced among conception and purposes to supply an in-depth exam of the innovations at the back of the advanced rules offered. within the ultimate part, Kapitaniak brings jointly chosen reprinted papers that have had an important influence at the improvement of this swiftly turning out to be interdisciplinary box. Controlling Chaos is key analyzing for graduates, researchers, and scholars wishing to be on the leading edge of this fascinating new department of science.
* makes use of effortless examples which are repeated through the reader either experimentally and numerically
* the 1st ebook to provide uncomplicated tools of controlling chaos
* comprises reprinted papers representing basic contributions to the field
* Discusses implementation of chaos controlling basics as utilized to useful difficulties
Read Online or Download Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics PDF
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Additional info for Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics
Um]T, f = [h,(u),... ,hm(u)] v, y -[u,+,,... ,u,] v, g -[hm+,(u),... 3) are called a driving subsystem and the third one a response subsystem. Lyapunov exponents of the response subsystem for a particular input x(t) are called conditional Lyapunov exponents. Let y(t) be a chaotic trajectory with initial condition y(0) and z'(t) be a trajectory starting in the nearby point z'(0). It was shown that the necessary and sufficient condition for I z(t) - y(t) l ~ 0 that is, the two subsystems being synchronized, is that all of the conditional Lyapunov exponents must be negative.
1 Idea of OPF method. 2 Controlling procedure using OPE therefore is fast and efficient. Processing here means detecting the position of a one-dimensional projection of a Poincar6 map, which can be accomplished by window comparators and track-and-hold circuitry. , 1992). Another engineering modification of OGY method, the bang-bang control, is described in Galias and Ogorzalek (1995). 3 Sampled input waveform method A very simple, robust and effective method of chaos control in terms of stabilization of an unstable periodic orbit has been proposed by Dedieu and Ogorzalek (1994).
In this procedure chaotic signals in the transmitter and receiver systems must be synchronized. As this way of sending information is difficult to unmask, it is called secure communication. 18. , 1993). 18). Transmitter l(t) , ,, _(5L5__;__; l(t) + n(t) n(t) . . UI. _ ,,L ,~ ' , ,,*, ': , ,! ,,,," v~ /, ',', J, /ii/ ~"i' ~/ :,/ Transmitter ,~. t ~ ' . ~i"~ /i~/ii~ i i/~tii ii' i i i l(t) + n(t) Received signal ,,~ ~,~ i '~ ' ~). 18 Idea of secure communication. signal. The first experimental application of this way of communication was reported by Parlitz et al.
Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics by Tomasz Kapitaniak