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Memorized Discrete Systems and Time-delay

Part of the Nonlinear Systems and Complexity Book Series (volume 17)

DOI: 10.1007/978-3-319-42778-2

ISBN: 978-3-319-42777-5

Publisher: Springer International Publishing - Springer Journals

Nov 20, 2016

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Chapter 1Memorized Linear Discrete Systems

Luo, Albert C. J.

Pages: 1 –50

[In this chapter, the basic iterative solutions for memorized linear discrete systems will be presented. The iterative solutions of the memorized linear discrete systems with distinct and repeated eigenvalues will be discussed. The stability of memorized linear discrete systems will be discussed...
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Chapter 2Memorized Nonlinear Discrete Systems

Luo, Albert C. J.

Pages: 51 –114

[In this chapter, basic concepts of memorized nonlinear discrete systems will be presented. The local theory of stability and bifurcation for memorized nonlinear discrete systems will be discussed.]
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Chapter 3Discretization of Time-delay Systems

Luo, Albert C. J.

Pages: 115 –220

[In this chapter, the discretization of time-delay continuous systems will be presented through time-delay and nontime-delay discrete nodes. The explicit and implicit discrete maps will be discussed for numerical predictions of time-delayed continuous systems. Basic discrete schemes are presented...
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Chapter 4Periodic Flows in Time-delay Systems

Luo, Albert C. J.

Pages: 221 –270

[This chapter will present periodic flowsPeriodic Flow in nonlinear time-delay dynamical systems through the discrete implicit mappings. The period-1 flows in nonlinear time-delay dynamical systems will be discussed first by the one-step discrete maps, and then the period-m flows in nonlinear...
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Chapter 5Time-Delayed Duffing Oscillator

Luo, Albert C. J.

Pages: 271 –296

[In this chapter, bifurcation trees of periodic motions in a periodically forced, time-delayed, Duffing oscillator are predicted by a semi-analytical method. From the finite discrete Fourier series, harmonic frequency–amplitude curves for stable and unstable period-1 to period-4 motions are...

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