Name: Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems (en Inglés)
Price: 204488.00 COP
Availability: InStock
Author: Xing, Siyuan ; Luo, Albert C. J.
ISBN: 9783031796685

portada Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems (en Inglés)

Formato

Libro Físico

Autor

Albert C. J. Luo

Siyuan Xing

Editorial

Springer

Idioma

Inglés

N° páginas

Encuadernación

Tapa Blanda

ISBN13

9783031796685

N° edición

Categorías

Diseño de productos
Diseño técnico
Ingeniería mecánica
Ingeniería eléctrica

Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems (en Inglés)

Albert C. J. Luo (Autor) · Siyuan Xing (Autor) · Springer · Tapa Blanda

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Reseña del libro "Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems (en Inglés)"

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.