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007			cr nn 008mamaa
008			220601s2020 sz | o |||| 0|eng d
020			_a9783031796692
024	7		_a10.1007/978-3-031-79669-2 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aQA427 _b2020 EB
100	1		_aXing, Siyuan _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9687813
245	1	0	_aSequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems _cby Siyuan Xing, Albert C. J. Luo
250			_a1st edition 2020
264		1	_aCham _bSpringer International Publishing _c2020
300			_a1 recurso en línea (XIII, 73 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Mechanical Engineering _x2573-3176
505	0		_aPreface -- Introduction -- A Semi-Analytical Method -- Periodic Motions in Time-Delay Systems -- A Global Sequential Scenario -- Frequency-Amplitude Analysis -- Global Sequential Periodic Motions -- Conclusive Remarks -- References -- Authors' Biographies.
520			_aIn 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.
988			_aSynthesis Collection of Technology_2020
650		7	_2embne _9667714 _aSistemas no lineales
650		7	_2embne _9666962 _aEcuaciones diferenciales no lineales _xSoluciones numéricas
700	1		_aLuo, Albert C. J. _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _998014
776	0	8	_iPrinted edition: _z9783031796708
776	0	8	_iPrinted edition: _z9783031796685
776	0	8	_iPrinted edition: _z9783031796715
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-79669-2 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b03/2023 _dz _eb _zSI