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Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points

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Abstract

Recently, systems with infinite equilibria have attracted interest because they can be considered as systems with hidden attractors. In this work, we introduce a new elegant system with an open curve of equilibrium points. It has just one parameter (a) and an exponential function. We show the dynamics of such a new chaotic oscillator by computing the Lyapunov exponents’ spectrum and bifurcation diagram, and it is implemented by using a field-programmable gate array (FPGA). The exponential function is approached by power series and then implemented with adders and multipliers within the FPGA. Experimental results are provided for the attractor as well as for the synchronization of two chaotic oscillators to transmit an image, thus demonstrating the usefulness of the new oscillator in a chaotic secure communication system.

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Acknowledgements

The authors want to thank to CONACyT/Mexico for the funding support under the project number 237991.

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Authors and Affiliations

  1. Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Puebla, Mexico

    Esteban Tlelo-Cuautle & Antonio de Jesus Quintas-Valles

  2. Department of Computer Sciences, CINVESTAV, Mexico City, Mexico

    Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga

  3. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

  4. Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Christos Volos

  5. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875–4413, Iran

    Sajad Jafari

Authors
  1. Esteban Tlelo-Cuautle
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  2. Luis Gerardo de la Fraga
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  3. Viet-Thanh Pham
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  4. Christos Volos
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  6. Antonio de Jesus Quintas-Valles
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Correspondence to Esteban Tlelo-Cuautle.

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Tlelo-Cuautle, E., de la Fraga, L.G., Pham, VT. et al. Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points. Nonlinear Dyn 89, 1129–1139 (2017). https://doi.org/10.1007/s11071-017-3505-2

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  • DOI: https://doi.org/10.1007/s11071-017-3505-2

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