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Experimental Verification of Optimized Multiscroll Chaotic Oscillators Based on Irregular Saturated Functions

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  • J. M. Muñoz-Pacheco
  • D. K. Guevara-Flores
  • O. G. Félix-Beltrán
  • E. Tlelo-Cuautle
  • J. E. Barradas-Guevara
  • C. K. Volos

Abstract

Multiscroll chaotic attractors generated by irregular saturated nonlinear functions with optimized positive Lyapunov exponent are designed and implemented. The saturated nonlinear functions are designed in an irregular way by modifying their parameters such as slopes, delays between slopes, and breakpoints. Then, the positive Lyapunov exponent is optimized using the differential evolution algorithm to obtain chaotic attractors with 2 to 5 scrolls. We observed that the resulting chaotic attractors present more complex dynamics when different patterns of irregular saturated nonlinear functions are considered. After that, the optimized chaotic oscillators are physically implemented with an analog discrete circuit to validate the use of proposed irregular saturated functions. Experimental results are consistent with MATLAB™ and SPICE circuit simulator. Finally, the synchronization between optimized and nonoptimized chaotic oscillators is demonstrated.

Suggested Citation

  • J. M. Muñoz-Pacheco & D. K. Guevara-Flores & O. G. Félix-Beltrán & E. Tlelo-Cuautle & J. E. Barradas-Guevara & C. K. Volos, 2018. "Experimental Verification of Optimized Multiscroll Chaotic Oscillators Based on Irregular Saturated Functions," Complexity, Hindawi, vol. 2018, pages 1-17, March.
    • Handle: RePEc:hin:complx:3151840
    DOI: 10.1155/2018/3151840
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    References listed on IDEAS

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    1. Xu, Yong & Gu, Rencai & Zhang, Huiqing, 2011. "Effects of random noise in a dynamical model of love," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 490-497.
    2. Ma, Yingjie & Li, Ya & Jiang, Xiling, 2015. "Simulation and circuit implementation of 12-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 127-133.
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    Cited by:

    1. Omar Guillén-Fernández & María Fernanda Moreno-López & Esteban Tlelo-Cuautle, 2021. "Issues on Applying One- and Multi-Step Numerical Methods to Chaotic Oscillators for FPGA Implementation," Mathematics, MDPI, vol. 9(2), pages 1-14, January.
    2. Ren, Guodong & Xue, Yuxiong & Li, Yuwei & Ma, Jun, 2019. "Field coupling benefits signal exchange between Colpitts systems," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 45-54.
    3. Wang, Haijun & Dong, Guili, 2019. "New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 272-286.
    4. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    5. Manoj Joshi & Vivek Bhatt & Ashish Ranjan, 2023. "A single parametrically controlled megastable multiscroll attractor with an unstable node," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(5), pages 1-9, May.

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