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Periodic Flows to Chaos in Time-delay Systems

Part of the Nonlinear Systems and Complexity Book Series (volume 16)

DOI: 10.1007/978-3-319-42664-8

ISBN: 978-3-319-42663-1

Publisher: Springer International Publishing - Springer Journals

Sep 18, 2016

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Chapter 1Linear Time-Delay Systems and Stability

Luo, Albert C. J.

Pages: 1 –33

[In this chapter, the theory of linear time-delay systems will be presented. Separated linear systems and diagonalization of square matrix will be discussed first. ]
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Chapter 2Nonlinear Time-Delay Systems

Luo, Albert C. J.

Pages: 35 –79

[In this chapter, the basic theory of nonlinear time-delay dynamical systems will be introduced. Local theory and bifurcation theory for nonlinear time-delay dynamical systems will be discussed. The stability switching and bifurcation on specific eigenvectors of the linearized, time-delayed...
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Chapter 3Periodic Flows in Time-Delay Systems

Luo, Albert C. J.

Pages: 81 –113

[In this chapter, from Luo (2014), periodic flows and chaos in nonlinear, time-delay dynamical systems will be presented.]
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Chapter 4Quasi-periodic Flows in Time-Delay Systems

Luo, Albert C. J.

Pages: 115 –155

[In this chapter, from Luo (2014), period-m flows to quasi-periodic flows in time-delayed nonlinear dynamical systems will be presented. The analytical solutions of quasi-periodic flows in autonomous time-delayed systems will be discussed, and the analytical solutions of quasi-periodic flows in...
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Chapter 5Time-Delay Duffing Oscillators

Luo, Albert C. J.

Pages: 157 –195

[In this chapter, periodic motions in a periodically excited Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis.]

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Periodic Flows to Chaos in Time-delay Systems

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