Implementation of Two Cell Non-Autonomous CNN Model on FPGA

Abstract

This paper presents implementation of a chaotic Cellular Neural Network (CNN) on Field Programmable Gate Array (FPGA). The network has two non-autonomous cells and exhibits chaotic behavior. In the implementation stage, Verilog Hardware Description Language (HDL) is used and discrete time model of the network is coded on Xilinx ISE Design Suite 13.2. It seems that the chaotic attractor can be used as entropy source or short key (seed) of chaos based random number generator design.

Keywords

• Cellular Neural Network,Chaos,FPGA,Random Number Generator

References

1. 1. Strogatz S.H., Herbert D.E., (1996). Nonlinear dynamics and chaos. Medical Physics-New York-Institute of Physics, 23(6), 993-995. 2. Natsheh A.N., Al-Habibah E.M.S., (2015). Chaos control DC-DC boost converter by FPGA. 2015 IEEE 42nd Photovoltaic Specialist Conference (PVSC), New Orleans, LA, 1-6. 3. Hidalgo R.M., Fernndez J.G., Rivera R.R., Larrondo H.A., (2001). Versatile dsp-based chaotic communication system. Electronic Letters, 37, 1204–1205. 4. Ali-Pacha A., Said N.H., M’Hamed A., Belgoraf A., (2007). Lorenz’s attractor applied to the stream cipher (alipacha generator). Chaos, Solitons and Fractals, 33(5), 1762-1766. 5. Mazzini G., Setti G., Rovatti R., (1997). Chaotic complex spreading sequences for aynhchronous ds-cdma-part 1: System modeling and results. IEEE Trans. Circuits Sys. 1, 44(10), 937–947. 6. Setti G., Balestra M., Rovatti R., (2000). Experimental verification of enhanced electromagnetic compatibility in chaotic fm clock signals. in Proceedings of ISCAS’00. IEEE Circuits and Systems Society, III-229–232. 7. Gonz´alez C.M., Larrondo H.A., Gayoso C.A., Arnone L.J., (2003). Generaci´on de secuencias binarias pseudo aleatorias por medio de un mapa ca´otico 3d. in Proceedings del IX Workshop de IBERCHIP. 8. De Micco L., Zabaleta O.G., Gonzlez C.M., Arizmendi C.M., Larrondo H.A., (2010). Estocasticidad de un atractor catico determinista implementado en fpga. Proceedings Iberchip. 9. De Micco L., Larrondo H.A., (2011). FPGA implementation of a chaotic oscillator using RK4 method. 2011 VII Southern Conference on Programmable Logic (SPL), Cordoba, 185-190.doi: 10.1109/SPL.2011.5782646. 10. Merah L., Ali-Pacha A., Said N.H., Mamat M., (2013). Design and FPGA implementation of Lorenz chaotic system for information security issues. Applied Mathematical Sciences, 7(5), 237-246. 11. Chua L.O., Yang L., (1988). Cellular neural networks: Theory. IEEE Trans. Circuits Syst., 35, 1257-1272. 12. Chua L.O., Yang L., (1988). Cellular neural networks: applications. IEEE Transactions on Circuits and Systems, 35(10), 1273-1290. 13. Zou F., Nossek J.A., (1993). Bifurcation and chaos in cellular neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(3), 166-173. 14. Zou F., Nossek J.A., (1991). A chaotic attractor with cellular neural networks. in IEEE Transactions on Circuits and Systems, 38(7), 811-812. 15. Gerosa A., Bernardini R., Pietri S., (2001). A fully integrated 8-bit, 20MHz, truly random numbers generator, based on a chaotic system. In: Proceedings of the Southwest Symposium on Mixed-Signal Design, SSMSD, 87–92. 16. Karakaya B., Yeniceri R., Yalcin M.E., (2015). Wave computer core using fixed-point arithmetic. 2015 IEEE International Symposium on Circuits and Systems (ISCAS), Lisbon, 1514-1517.