Jacques M. Bahi, Christophe Guyeux's Discrete Dynamical Systems and Chaotic Machines: Theory and PDF

By Jacques M. Bahi, Christophe Guyeux

ISBN-10: 1466554509

ISBN-13: 9781466554504

For machine scientists, in particular these within the safeguard box, using chaos has been constrained to the computation of a small number of recognized yet flawed maps that supply no clarification of why chaos is correct within the thought of contexts. Discrete Dynamical platforms and Chaotic Machines: conception and functions shows the right way to make finite machines, resembling desktops, neural networks, and instant sensor networks, paintings chaotically as outlined in a rigorous mathematical framework. taking into consideration that those machines needs to engage within the actual global, the authors percentage their examine effects at the behaviors of discrete dynamical platforms and their use in laptop technology.

Covering either theoretical and sensible points, the booklet presents:

  • Key mathematical and actual principles in chaos concept
  • Computer technological know-how basics, essentially developing that chaos homes may be chuffed through finite nation machines
  • Concrete functions of chaotic machines in laptop defense, together with pseudorandom quantity turbines, hash features, electronic watermarking, and steganography
  • Concrete purposes of chaotic machines in instant sensor networks, together with safe information aggregation and video surveillance

Until the authors’ contemporary study, the sensible implementation of the mathematical thought of chaos on finite machines raised a number of concerns. This self-contained ebook illustrates how chaos thought allows the examine of computing device protection difficulties, resembling steganalysis, that another way couldn't be tackled. It additionally explains how the idea reinforces present cryptographically safe instruments and schemes.

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Additional resources for Discrete Dynamical Systems and Chaotic Machines: Theory and Applications

Sample text

4 Perfect discrete dynamical systems . . . . . . . . . . . . . . 3 Stability, Sensitivity, and Expansiveness . . . . . . . . . . . . . . . 1 Stability and instability . . . . . . . . . . . . . . . . . . . . 2 Sensitivity to the initial conditions . . . . . . . . . . . . . . 3 Expansiveness . . . . . . . . . . . . . . . . . . . . . . . . . 1 Definition . . . . . . . . .

2 Simplification of Discrete Dynamical Systems . . . . . . . . . . . . 1 Invariant subsystems . . . . . . . . . . . . . . . . . . . . . . 2 (Un)decomposability and transitivity . . . . . . . . . . . . . 1 Decomposability . . . . . . . . . . . . . . . . . . . 2 Transitivity . . . . . . . . . . . . . . . . . . . . . . 3 Consequences of the transitivity property . . . .

1 (n, ε)-covers . . . . . . . . . . . . . . . . . . . . . . 2 Topological entropy . . . . . . . . . . . . . . . . . . 4 Properties of the topological entropy . . . . . . . . . . . . . 37 38 38 38 39 39 40 40 40 41 41 42 42 42 43 Chaotic dynamical systems have too complex behavior to be able to encompass all of their aspects using a single “perfect” definition. Indeed there exist several notions of chaos, each of them emphasize one clearly defined aspect of a chaotic behavior.

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Discrete Dynamical Systems and Chaotic Machines: Theory and Applications by Jacques M. Bahi, Christophe Guyeux


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