Journals / International Advanced Researches and Engineering Journal / 2018 / Cilt: 2 - Sayı: 2

Selection of optimal numerical method for implementation of Lorenz Chaotic system on FPGA

Pages
147–152
Publication Date
2022-10-19
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The optimal numerical method based on application area is proposed by proving accuracy and complexity of methods and comparing designs in terms of resource utilizations on FPGA board.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, implementation of Lorenz chaotic system on Spartan 3e XC3S1600e FPGA development board by using Xilinx System Generator technology is presented.
📊
Key Findings & Data:Differential equations of any nonlinear system have to be discretized before coding and design process on FPGA editor.
💡
Conclusion & Impact:The optimal numerical method based on application area is proposed by proving accuracy and complexity of methods and comparing designs in terms of resource utilizations on FPGA board.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Chaos · FPGA · Lorenz chaotic system

Abstract

In this study, implementation of Lorenz chaotic system on Spartan 3e XC3S1600e FPGA development board by using Xilinx System Generator technology is presented. Differential equations of any nonlinear system have to be discretized before coding and design process on FPGA editor. The Lorenz chaotic system is discretized by using Taylor series expansion, Runge-Kutta and Euler discretization methods which are mostly preferred to discretize the continuous formed signals. The optimal numerical method based on application area is proposed by proving accuracy and complexity of methods and comparing designs in terms of resource utilizations on FPGA board.

🔖

Cite This Article

GÜLTEN, A., TÜRK, M. A., KARAKAYA, B., TÜRK, M. (2022). Selection of optimal numerical method for implementation of Lorenz Chaotic system on FPGA. International Advanced Researches and Engineering Journal, Cilt: 2 - Sayı: 2, 147–152. https://ajindex.com/articles/539387

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Zirkohi, M.M., Model reference type-2 fuzzy sliding mode control for a novel uncertain hyperchaotic system, Journal of Intelligent & Fuzzy Systems, 32 (1); 389-400, 2017
  2. Jia, N., Wang, T., Chaos control and hybrid projective synchronization for a class of new chaotic systems, Computers & Mathematics with Applications, 62 (12); 4783-4795, 2011
  3. Lorenz, E.N., Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences, 20; 130-141, 1963
  4. Hilborn, R.C., Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press, 1994
  5. Li, C., Sprott, J.C., Thio, W., Linearization of the Lorenz system, Physics Letters A, 379 (10); 888-893, 2015
  6. Yang, S.K., Chen, C.L., Yau, H.T., Control of chaos in Lorenz system, Chaos, Solitons & Fractals, 13 (4); 767-780, 2002
  7. Leonov, G.A., Kuznetsov, N.V., On differences and similarities in the analysis of Lorenz, Chen and Lu systems, Applied Mathematics and Computation, 256; 334-343, 2015
  8. Chen, D., Sun, Z., Ma, X., Chen, L., Circuit implementation and model of a new multi-scroll chaotic system, International Journal of Circuit Theory and Applications, 42 (4); 407-424, 2014
  9. Li, Y., Liu, X., Chen, G., Liao, X., A new hyperchaotic Lorenz-type system: Generation, analysis, and implementation, International Journal of Circuit Theory and Applications, 39 (8); 865-879, 2011
  10. Ma, J., Wang, L., Duan, S., Xu, Y., A multi-wing butterfly chaotic system and its implementation, International Journal of Circuit Theory and Applications, doi: 10.1002/cta.2357, 2017
  11. Tlelo-Cuautle, E., Rangel-Magdaleno, J.J., Pano-Azucena, A.D., Obeso-Rodelo, P.J., Nuñez-Perez, J.C., FPGA realization of multi-scroll chaotic oscillators, Communications in Nonlinear Science and Numerical Simulation, 27 (1); 66-80, 2015
  12. Merah, L., Ali-Pacha, A., Said, N.H., Mamat, M., Design and FPGA implementation of Lorenz chaotic system for information security issues, Applied Mathematical Sciences, 7 (5); 237-246, 2013
  13. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A., Determining Lyapunov exponents from time series, Physica D: Nonlinear Phenomena, 16 (3); 285-317, 1985
  14. Rosenstein, M.T., Collins, J.J., De Luca, C.J., A practical method for calculating largest Lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena, 65 (1); 117-134, 1993
  15. Xilinx Inc., System Generator for Digital Signal Processing, http://www.xilinx.com / tools / dsp.htm
  16. Karakaya, B., Yeniceri,