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Chaos / Volume 21 / Issue 4 / FOCUS ISSUE: NONLINEAR AND STOCHASTIC PHYSICS IN BIOLOGY

Chaos 21, 047520 (2011); http://dx.doi.org/10.1063/1.3664349 (9 pages)

Unstable periodic orbits and noise in chaos computing

Behnam Kia1,2, Anna Dari1, William L. Ditto1, and Mark L. Spano1

1School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85287-9709, USA
2School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA

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(Received 19 August 2011; accepted 8 November 2011; published online 29 December 2011)

Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. CHAOS COMPUTING: THE CENTRAL CONCEPT
  3. DEALING WITH NOISE FROM CHAOTIC SADDLES
  4. UPO-BASED MODEL FOR MODELING CHAOS COMPUTING AND NOISE EFFECTS
  5. TIME SERIES
    1. Extracting a partition from the time series
    2. Extracting UPOs from time series
    3. Extracting the neighborhoods of the UPOs
    4. Extracting the eigenvalues and estimating robustness
    5. Forecasting chaotic orbits to compute the minimum distance from partition boundaries
    6. Putting it all together
  6. CONCLUSIONS

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KEYWORDS and PACS

Keywords

biomedical communication, chaotic communication, Chua's circuit, logic circuits, noise measurement, nonlinear dynamical systems, symbol manipulation, time series

PACS

  • 84.30.Sk

    Pulse and digital circuits

  • 02.70.Wz

    Symbolic computation (computer algebra)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3664349

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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