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

Yıl 2018, Cilt: 2 Sayı: 2, 147 - 152, 15.08.2018

Barış Karakaya , Meral Akarçay Türk Mustafa Türk , Arif Gülten

Öz

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.

Anahtar Kelimeler

Chaos, FPGA, Lorenz chaotic system, Numerical Methods

Kaynakça

• 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, R., Yalçın M.E., Wave computer core using fixed-point arithmetic, 2015 IEEE International Symposium on Circuits and Systems (ISCAS), 1514-1517, 2015.