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Chaotic Synchronization and Its Applications in Secure Communications

  • Rafael Martínez-GuerraEmail author
  • Juan L. Mata-Machuca
  • Ricardo Aguilar-López
  • Andrés Rodríguez-Bollain
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

This work deals with the chaotic synchronization of a class of nonlinear systems and some applications (e.g., temperature regulation of chaotic chemical systems, secure communications). We present two approaches, the first one is based on observer design theory in a master-slave configuration, thus, chaos synchronization problem can be posed as an observer design procedure, where the coupling signal is viewed as measurable output and the slave system is regarded as observer. Some results of the differential and algebraic framework are applied in order to determine if the system is observable and parameters are identifiable with the available output. As applications of this technique we show the synchronization and parameter estimation of the Colpitts oscillator considered as a Chaotic Liouvillian System (CLS) in a real-time implementation; other example is shown by using an sliding-mode uncertainty observer which allows us to achieve secure communications. The second approach is related with the feedback control design, the aim of this technique is the synthesis of a robust control law for the control of CLS, we apply this method to a class of chaotic Liouvillian chemical systems with success.

Keywords

Chaotic System Slave System Chaotic Synchronization Reduce Order Observer Colpitts Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Juan L. Mata-Machuca and Andrés Rodríguez-Bollain are grateful with CONACyT (Mexico) for the corresponding postgraduate scholarships.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rafael Martínez-Guerra
    • 1
    Email author
  • Juan L. Mata-Machuca
    • 1
  • Ricardo Aguilar-López
    • 2
  • Andrés Rodríguez-Bollain
    • 1
  1. 1.Departamento de Control AutomáticoCINVESTAV-IPNDistrito Federal, MéxicoMéxico
  2. 2.Departamento de Biotecnolog y BioingenieríaCINVESTAV-IPNDistrito Federal, MéxicoMéxico

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