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Circuit Realization of the Synchronization of Two Chaotic Oscillators with Optimized Maximum Lyapunov Exponent

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Advances in Chaos Theory and Intelligent Control

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 337))

Abstract

The modeling, simulation and circuit realization of the synchronization of two optimized multi-scroll chaotic oscillators is described herein. The case of study is the master-slave synchronization of two multi-scroll chaotic oscillators generating four to seven scrolls, based on saturated function series. The maximum Lyapunov exponent (MLE) of the chaotic oscillator is optimized by applying meta-heuristics. We show the behavior on the synchronization for chaotic oscillators with low and high MLEs, while the synchronization is performed by generalized Hamiltonian forms and observer approach from nonlinear control theory. Numerical simulation results are given for the chaotic oscillators with and without optimized MLEs, and for their master-slave synchronization. Finally, we show the good agreement between theoretical results, SPICE simulations and the experimental results when the whole synchronized system is implemented with commercially available operational amplifiers.

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Acknowledgments

The first author wants to thank CONACyT-Mexico for the scholarship 331697. This work has been partially supported by CONACyT-Mexico under grant 237991-Y, in part by the TEC2013-45638-C3-3-R, funded by the Spanish Ministry of Economy and Competitiveness and ERDF, by the P12-TIC-1481 project, funded by Junta de Andalucia, and by CSIC project PIE 201350E058.

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Authors and Affiliations

  1. INAOE, Puebla, Mexico

    V. H. Carbajal-Gómez & E. Tlelo-Cuautle

  2. Instituto de Microelectronica de Sevilla, IMSE-CNM, CSIC, University of Seville, Seville, Spain

    F. V. Fernández

Authors
  1. V. H. Carbajal-Gómez
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  2. E. Tlelo-Cuautle
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  3. F. V. Fernández
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Corresponding author

Correspondence to E. Tlelo-Cuautle .

Editor information

Editors and Affiliations

  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Carbajal-Gómez, V.H., Tlelo-Cuautle, E., Fernández, F.V. (2016). Circuit Realization of the Synchronization of Two Chaotic Oscillators with Optimized Maximum Lyapunov Exponent. In: Azar, A., Vaidyanathan, S. (eds) Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-30340-6_26

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  • DOI: https://doi.org/10.1007/978-3-319-30340-6_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30338-3

  • Online ISBN: 978-3-319-30340-6

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