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Discrete Dynamical Systems and Chaotic Machines: Theory and Applications

Jacques M. Bahi and Christophe Guyeux
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2013
Number of Pages: 
212
Format: 
Hardcover
Series: 
Chapman & Hall/CRC Numerical Analysis and Scientific Computing
Price: 
89.95
ISBN: 
9781466554504
Category: 
Monograph
We do not plan to review this book.

An Introduction to Chaos
Classical Examples by Way of Introduction
Historical Context
Feigenbaum’s Bifurcation
The Logistic Map
The Lorenz System

The Mathematical Theory of Chaos
Definitions and Notations

Topological and Metrical Spaces
Compactness and Completeness
Continuity
Discrete Dynamical Systems

Devaney’s Formulation of Chaos
Periodicity, Stability, and Regularity
Simplification of Discrete Dynamical Systems
Stability, Sensitivity, and Expansiveness
Chaos as Defined by Devaney (1989)
Examples of Chaotic Systems
Topological and Metrical Conjugacies

Other Formulations of Chaos
The Lyapunov Exponent
Topological and Metrical Entropy

From Theory to Practice
A Fundamental Tool: the Chaotic Iterations

Introducing the Chaotic Iterations
Chaotic Iterations as Devaney’s Chaos
Topological Properties of Chaotic Iterations
Characterization
The Lyapunov Exponent

Theoretical Proofs of Chaotic Machines
Chaotic Turing Machines
Practical Issues

Applications of Chaos in the Computer Science Field
Information Security

Steganography and Digital Watermarking
Pseudorandom Number Generators
Hash Functions

Wireless Sensor Networks
Video Surveillance
Secure Aggregation

Conclusion
Conclusion

Synthesis
Perspectives

Bibliography

Index

Dummy View - NOT TO BE DELETED