By Tomasz Kapitaniak
Greater than twenty years of in depth reviews on non-linear dynamics have raised questions about the sensible functions of chaos. One attainable solution is to manage chaotic habit in a predictable approach. This e-book, oneof the 1st at the topic, explores the guidelines in the back of controlling chaos.
Controlling Chaos explains, utilizing basic examples, either the mathematical thought and experimental effects used to use chaotic dynamics to genuine engineering platforms. Chuas circuit is used to illustrate during the e-book because it might be simply built within the laboratory and numerically modeled. using this instance permits readers to check the theories provided. The textual content is punctiliously balanced among conception and purposes to supply an in-depth exam of the techniques at the back of the advanced rules offered. within the ultimate part, Kapitaniak brings jointly chosen reprinted papers that have had an important impact at the improvement of this swiftly growing to be interdisciplinary box. Controlling Chaos is vital studying for graduates, researchers, and scholars wishing to be on the vanguard of this interesting new department of science.
* makes use of effortless examples which might be repeated through the reader either experimentally and numerically
* the 1st booklet to offer simple equipment of controlling chaos
* comprises reprinted papers representing basic contributions to the field
* Discusses implementation of chaos controlling basics as utilized to sensible difficulties
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Extra info for Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics
1I 0 0 9 . . 9 . . . . . 8 Stability map of the rotor system. When o~ is near to co,, we may diminish K~ from 22 to 14. 55. When o~ is bigger than o~2, we may change K~ again. The change of K, may be realized by the use of an additional springs K,2. 3) In the range o~, < co < o~2,the connection points are released, and both (top and bottom) springs go into action. 4) We have described the controlling method which allows control of Hopf bifurcation in transients. This method guarantees the passage through the unstable zone between the Hopf and reversed Hopf bifurcation points.
It will tend to persist in synchronized states. 2 ' ' ' ' I ' ' ' ! ' ! | ! [ ! ! i ! 17); (a) transient evolution (b) synchronized state. 6 Secure communication Chaos synchronization allows applications of chaotic systems to mask the information signal l(t) by adding it to a larger chaotic signal n(t) and transmitting the superposition of both signals. Information can be recovered after the comparison of the received signal l(t) + n(t) with the original chaotic noise n(t). In this procedure chaotic signals in the transmitter and receiver systems must be synchronized.
1987) Control of a system with a strange attractor through periodic parametric action. Sov. Phys. , 32, 1346-1348. A. D. (1995) Chaotic synchronization of mutuallycoupled generators with frequency-controlled feedback loop. Int. J. Bifurcat. Chaos, 5, 551-558. E. A. (1991) Forced and mutual synchronization of chaos. Radioeng. Electron. 36, 338351. Azevedo, A. M. (1991) Controlling chaos in spin-wave instabilities. Phys. Rev. , 66, 1342-1345. W. B. (1980) Chaotic motion in nonlinear feedback systems.
Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics by Tomasz Kapitaniak