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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Technik Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems
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Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems
Siyuan Xing, Albert C.J. Luo (Broschiert, Englisch)
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Beschreibung
In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of… the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy.
The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems. 29,95 €
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Technische Daten
Erscheinungsdatum
11.09.2020
Sprache
Englisch
EAN
9783031796685
Herausgeber
Springer International Publishing
Titel in Originalsprache
Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems
Serien- oder Bandtitel
Synthesis Lectures on Mechanical Engineering
Sonderedition
Nein
Autor
Siyuan Xing, Albert C.J. Luo
Seitenanzahl
73
Auflage
1
Hersteller: Springer Nature Customer Service Center GmbH, ProductSafety@springernature.com
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