DIGITALLY PROGRAMMABLE MULTI-SCROLL CHAOS GENERATOR ON FPGA

Yıl 2020, Cilt: 10 Sayı: 2, 207 - 216, 30.12.2020

Barış Karakaya , Fatma Çulcu , Mustafa Türk

https://doi.org/10.36222/ejt.674358

Cited By: 1

Öz

Multi-scroll chaotic attractors exhibit higher unpredictability than double-scroll attractors. However, the more number of scrolls cost the more usage of sources. To overcome this problem, the attractor design should be simplified. This paper presents a systematic approach that enables to realize digital piece wise linear (PWL) function in nonlinear dynamical system and to obtain whole behaviors in only one model. The proposed design requires only number of scroll as input and can realize chaotic PWL signal with a fewer number of FPGA resources. In the implementation stage of the study, the discrete mathematical equations of the chaotic attractor is modelled in Xilinx System Generator (XSG) platform and realized by using Xilinx Kintex-7 KC705 Evaluation Board.

Anahtar Kelimeler

chaos, discrete time, multi-scroll, xilinx system generator

Kaynakça

• [1] Strogatz, S. H., Herbert, D. E., “Nonlinear dynamics and chaos”, Medical Physics-New York-Institute of Physics, Vol. 23(6), pp. 993-995, 1996.
• [2] Lorenz, E.N., “Deterministic Nonperiodic Flow”, Journal of the Atmospheric Sciences, Vol. 20; pp. 130-141, 1963.
• [3] Hilborn, R.C., Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press, 1994.
• [4] Li, C., Sprott, J.C., Thio, W., “Linearization of the Lorenz system”, Physics Letters A, Vol. 379 (10); pp. 888-893, 2015.
• [5] Chua, L.O., “The genesis of Chua’s circuit”, Archiv fur Elektronik and Ubertragungstechnik, Vol. 46(4), pp. 250-257, 1992.
• [6] Zhong, G., Man, K., Chen, G., “A systematic approach to generating n-scroll attractors”, International Journal of Bifurcation and Chaos, Vol. 12(12), pp. 2907-2915, 2002.
• [7] 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, Vol. 27 (1), pp. 66-80, 2015.
• [8] Genesio, R., Tesi, A., “Distorsion control of chaotic systems: the chua's circuit in R. N. Madan (ed.), Chua's circuit: a paradigm for chaos”, World Scientific Series on Nonlinear Sciences Series B, Vol. 1, pp. 514-534, 1993.
• [9] Hartley, T., Mossayebi, F., “Control of chua's circuit, in R. N. Madan (ed.), Chua's circuit: a paradigm for chaos”, World Scientific Series on Nonlinear Sciences, Series B, Vol. 1, pp. 492-513, 1993.
• [10] Hwang, C. C., Chow, H., Wang, Y. “A new feedback control of a modified chuas circuit system”, Physica D, Vol. 92, pp. 95-100, 1996.
• [11] Lee, B.-C., Lee, H.-H., Wang, B.-H., “Control bifurcation structure of return map control in chua's circuit”, International Journal of Bifurcation and Chaos, Vol. 7,(4), pp. 903-909, 1997.
• [12] Li, Z. G., Wen, C. Y., Soh, Y. C., Xie, W. X., “The stabilization and synchronization of chua's oscillators via impulsive control”, IEEE Transactions on circuits and systems I, Vol. 48(11), pp. 1351-1355, 2001.
• [13] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., Zhou, C. S., “The synchronization of chaotic systems”, Physics Reports, Vol. 366, pp. 1-101, 2002.
• [14] Pikovsky, A., Rosenblum, M., Kurths, J., Synchronization: A universal concept in nonlinear sciences, Cambridge Nonlinear Science Series 12, 2001.
• [15] Pecora, L. M., Carroll, T. L., “Synchronization in chaotic systems”, Physical Review Letters, Vol. 64(8), pp. 821-824, 1990.
• [16] Suykens, J. K., Vandewalle, J., “Generation of n-double scrolls (n=1;2;3;4; ...)”, IEEE Transactions on Circuits and Systems I, Vol. 40, pp. 861-867, 1993.
• [17] Suykens, J. A. K., Huang, A., Chua, L. O., “A family of n-scroll attractors from a generalized chuas circuit”, Archiv fur Elektronik und Ubertragungstechnik, Vol. 51(3), pp. 131-138, 1997.
• [18] Yalcin, M. E., Suykens, J. A. K., Vandewalle, J., “Experimental confirmation of 3- and 5-scroll attractors from a generalized chua's circuit”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 47(3), pp. 425-429, 2000.
• [19] Tang, K. S., Zhong, G. Q., Chen, G., Man, K. F., “Generation of n-scroll attractors via sine function”, IEEE Transactions on Circuits and Systems I, Vol. 48, pp. 1369-1372, 2001.
• [20] Ozoguz, S., Elwakil, A. S., Salama, K. N., “n-scroll chaos generator using nonlinear transconductor”, Electronics Letters, Vol. 38, pp. 685-686, 2002.
• [21] Lü, J., Han, F., Yu, X., Chen, G., “Generating 3-d multiscroll chaotic attractors: A hysteresis series switching method”, Automatica, Vol. 40, pp. 1677-1687, 2004.
• [22] Kaya, D., Türk, M., A Matlab/Simulink model for multi-scroll chaotic attractors, 2015 23nd Signal Processing and Communications Applications Conference (SIU), Malatya, 2015, pp. 164-167, doi: 10.1109/SIU.2015.7130412.
• [23] Türk, M., Gülten, A., “Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique”, Simulation Modelling Practice and Theory, Vol. 19(3), pp. 899-910, 2011.
• [24] Karakaya, B., Akarçay Türk, M., Türk, M., Gülten, A., Selection of optimal numerical method for implementation of Lorenz Chaotic system on FPGA, International Advanced Researches and Engineering Journal , 2 (2) , 147-152, 2018.
• [25] Xilinx Inc., System Generator for Digital Signal Processing, http://www.xilinx.com / tools / dsp.htm.