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Dynamical System Synchronization

Part of the Nonlinear Systems and Complexity Book Series (volume 3)

DOI: 10.1007/978-1-4614-5097-9

ISBN: 978-1-4614-5096-2

Publisher: Springer New York - Springer Journals

Oct 23, 2012

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Chapter 1Introduction

Luo, Albert C. J.

Pages: 1 –9

[With human-being development and progress, coordinate systems are used in order that the characteristics and behaviors of everything in nature can be described quantitatively. In other words, because the coordinates systems are used extensively, one gradually understands and improves the...
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Chapter 2Discontinuity and Local Singularity

Luo, Albert C. J.

Pages: 11 –69

[In this chapter, a general theory for the passability of a flow to a specific boundary in discontinuous dynamical systems will be discussed. The concepts of real and imaginary flows will be introduced. The G-functions for discontinuous dynamical systems will be presented to describe the...
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Chapter 3Single Constraint Synchronization

Luo, Albert C. J.

Pages: 71 –120

[In this chapter, synchronization of two or more dynamical systems to specific constraints is introduced, which is different from the traditional synchronization of two dynamical systems. For such synchronization, Lyapunov stability method cannot be adopted. The synchronization,...
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Chapter 4Multiple Constraints Synchronization

Luo, Albert C. J.

Pages: 121 –155

[In this chapter, the synchronization of two dynamical systems to multiple constraints will be discussed. As in Luo [1], the synchronicity of two dynamical systems with multiple constraints can be presented. The mathematical description of the synchronicity of two dynamical systems to multiple...
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Chapter 5Function Synchronizations

Luo, Albert C. J.

Pages: 157 –195

[In this chapter, the theory of dynamical system synchronization will be applied to the function synchronization of two distinct dynamical systems. Periodic and chaotic synchronizations between two distinct dynamical systems under specific constraints will be investigated. The analytical...
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Chapter 6Discrete Systems Synchronization

Luo, Albert C. J.

Pages: 197 –236

[As in Luo [1, 2], a set of concepts on “Ying” and “Yang” in discrete dynamical systems will be presented. Based on the Ying-Yang theory, the complete dynamics of discrete dynamical systems will be presented for an understanding of dynamical behaviors. From the ideas of the Ying-Yang theory of...

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