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Regularity and Complexity in Dynamical Systems

Part of the Nonlinear Systems and Complexity Book Series (volume 1)

DOI: 10.1007/978-1-4614-1524-4

ISBN: 978-1-4614-1523-7

Publisher: Springer New York - Springer Journals

Sep 22, 2011

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Chapter 1Nonlinear Continuous Dynamical Systems

Luo, Albert C. J.

Pages: 1 –63

[In this Chapter, basic concepts of nonlinear dynamical systems will be presented as a review material. Local theory, global theory and bifurcation theory of nonlinear dynamical systems will be discussed. The stability switching and bifurcation on specific eigenvectors of the linearized system at...
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Chapter 2Nonlinear Discrete Dynamical Systems

Luo, Albert C. J.

Pages: 65 –136

[In this chapter, the basic concepts of nonlinear discrete systems will be presented. The local and global theory of stability and bifurcation for nonlinear discrete systems will be discussed. The stability switching and bifurcation on specific eigenvectors of the linearized system at fixed...
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Chapter 3Chaos and Multifractality

Luo, Albert C. J.

Pages: 137 –167

[In this Chapter, basic concepts of fractal in nonlinear dynamical systems will be presented as an introduction. The fractal generation rules will be presented for nonrandom and random fractals. The multifractals based on the single- and joint-multifractal measures will be presented....
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Chapter 4Complete Dynamics and Synchronization

Luo, Albert C. J.

Pages: 169 –221

[This chapter presents a Ying–Yang theory for nonlinear discrete dynamical systems with consideration of positive and negative iterations of discrete iterative maps. In existing analysis, the solutions relative to “Yang” in nonlinear dynamical systems are extensively investigated. However, the...
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Chapter 5Switching Dynamical Systems

Luo, Albert C. J.

Pages: 223 –296

[In this chapter, dynamics of switching dynamical systems will be presented. A switching system of multiple subsystems with transport laws at switching points will be discussed. The existence and stability of switching dynamical systems will be discussed through equi-measuring functions. The...
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Chapter 6Mapping Dynamics and Symmetry

Luo, Albert C. J.

Pages: 297 –363

[In the previous chapter, dynamics of switching systems were discussed. In this chapter, mapping dynamics and symmetry in discontinuous dynamical systems will be discussed. The G-function of the discontinuous boundary will be presented first. To understand of nonlinear dynamics of a flow from one...

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