FPGA Based Digital Implementation of Adaptive Synchronization Methodology for 6-D Chaotic System
AUTHORS
Rameshbabu Ramar,Research Scholar, St. Peter’s Institute of Higher Education and Research, India
G R Suresh,Professor, St. Peter’s Institute of Higher Education and Research, India
ABSTRACT
In this paper, we proposed the FPGA based digital implementation of synchronization methodology for 6-D chaotic systems via nonlinear feedback adaptive control technique. We derived new results for the adaptive controllers and the parameter update laws based on Lyapunov stability theory to achieve the synchronization between identical 6-D chaotic systems. Since the digitization of chaotic synchronization is necessary for digital communication, the proposed adaptive synchronization methodology is implemented in digital circuits based on Field Programmable Gate Array chip. The digital chaotic signal also generated using MATLAB simulink and Xilinx System Generator technology. The numerical simulation and FPGA outputs are used to prove the robustness and effectiveness of our proposed methodology.
KEYWORDS
Chaotic system, Adaptive synchronization, FPGA implementation
REFERENCES
[1] E. N. Lorenz, “Deterministic non periodic flow” ,Journal of Atmospheric Sciences, vol.20, pp.134, (1963) DOI: 10.1175/1520-0469 (CrossRef)(Google Scholar)
[2] G. Kaddoum, “Wireless Chaos-Based Communication Systems: A Comprehensive Survey,” IEEE Access, vol.4, pp.2621-2648, (2016) DOI:10.1109/ACCESS.2016.2572730(CrossRef)(Google Scholar)
[3] G. A. Abib and M. Eisencraf, “On the performance of a digital chaos-based communication system in noisy channels,” IFAC Papers online, vol.48, no.11, pp.976-981, (2015) DOI:10.1016/j.ifacol.2015.09.319(CrossRef)(Google Scholar)
[4] N. X. Quyen, “On the study of quadrature DCSK modulation scheme for coginitive radio,” International Journal of Bifurcation and Chaos, vol.27, no.09, 1750135, (2017) DOI: 10.1142/S0218127417501358(CrossRef)(Google Scholar)
[5] X. Gao, M. F. Cheng, L. Deng, M. Zhang, S. Fu, and D. Liu, “Robust chaotic - shift - keying scheme based on electro optical hybrid feedback system,” Optics Express, vol.28, no.08, pp.10847-10858, (2020) DOI: 10.1364/OE.389251(CrossRef)(Google Scholar)
[6] C. Bai, H.P. Ren, M.S. Baptista, and C. Grebogi, “Digital underwater communication with chaos,” Communications in Nonlinear Science and Numerical Simulation, vol.73, pp.14-24, (2019) DOI: 10.1016/j.cnsns.2019.01.02(CrossRef)(Google Scholar)
[7] L. L. Bonilla, M. Alvaro, and M. Carretero, “Chaos based true random number generators,” Journal of Mathematics in Industry, vol.7, no.1, (2016) DOI: 10.1186/s13362-016-0026-4 (CrossRef)(Google Scholar)
[8] M. Garcia-Bosque, A. Pérez-Resa, C. Sánchez-Azqueta, C. Aldea, and S. Celma, “Chaos-based bitwise dynamical pseudorandom number generator on FPGA,” IEEE Transactions on Instrumentation and Measurement, vol.68, no.1, pp.291-293, ( 2019) DOI:10.1109/TIM.2018.2877859(CrossRef)(Google Scholar)
[9] J. SenTeh, M. Alawida, and Y. Cheng Sii, “Implementation and practical problems of chaos based cryptography revisited,” Journal of Information Security and Applications, vol.50, (2019) DOI: 10.1016/j.jisa.2019.102421 (CrossRef)(Google Scholar)
[10] Y. Luo, J. Yu, W. Lai, and L. Liu, “ A novel chaotic image encryption algorithm based on improved baker map and logistic map,” Multimedia Tools and Applications, vol.78, pp.22023-22043, (2019) DOI: 10.1007/s11042-019-7453-3(CrossRef)(Google Scholar)
[11] Z. Hua, Y. Zhou, and H. Huang, “Cosine transform based chaotic system for image encryption,” Information Sciences, vol.480, pp.403-419 (2019) DOI: 10.1016/j.ins.2018.12.048(CrossRef)(Google Scholar)
[12] Salama, Wessam, Elkamchouchi, Hassan, Abouelseoud, and Yasmine, “New Video Encryption Schemes Based on Chaotic Maps,” IET Image Processing, vol.14, no.2, (2020) DOI: 10.1049/iet-ipr.2018.5250.(CrossRef)(Google Scholar)
[13] A.Ahmadi, K. Rajagopal, F.E. Alsaadi,V.T. Pham, F.E. Alsaadi, and S. Jafari, “A novel 5D chaotic system with extreme multi - stability and a line of equilibrium and its engineering applications: circuit design and FPGA implementation,” Iranian Journal of Science and Technology, Transaction of Electrical Engineering, vol.44, pp.59-67, (2020) DOI: 10.1007/s40998-019-00223-5(CrossRef)(Google Scholar)
[14] F. Yu, L. Liu, Binyong, Y. Huang, C. Shi, S. Cai, Y.Song, S. Du, and Q. Wan, “Analysis and FPGA realization of novel 5D hyperchaotic four wing memristor system, Active control synchronization and secure communication application,” Complexity, vol.2019, Article ID 4047957, (2019) DOI: 10.1155/2019/4047957(CrossRef)(Google Scholar)
[15] W.G. Yi, B.X. ei and W.Z. Lin, “Design and FPGA implementation of new hyperchaotic system,” Chinese Physics B, vol.17, no.10 (2008) DOI: 10.1088/1674-1056/17/10/011 (CrossRef)(Google Scholar)
[16] I. Koyuncu, A.T. Özcerit, and I. Pehlivan, “ Implementation of FPGA based real time novel chaotic oscillator,” Nonlinear Dynamics, vol.77, pp.49-9, (2014) DOI: 10.1007/s11071-014-1272-x(CrossRef)(Google Scholar)
[17] Z. Hua, B. Zhou, and Y. Zhou, “Sine-transform-based chaotic system With FPGA implementation,” in IEEE Transactions on Industrial Electronics, vol.65, no.3, pp.2557-2566, (2018) DOI: 10.1109/TIE.2017.2736515(CrossRef)(Google Scholar)
[18] M. Qiu, S.Yu, Y. Wen, J. Lü, J. He, andZ. Lin, “Design and FPGA implementation of a universal chaotic signal generator based on the verilog HDL fixed point algorithm and state machine control,” International Journal of Bifurcation and Chaos, vol.27, no.03, (2017) DOI: 10.1142/S0218127417500407(CrossRef)(Google Scholar)
[19] M. Lahcene, A. Adda, S. Naima Hadj, and M. Mustafa, “Design and FPGA implementation of Lorenz chaotic system for information security systems,” Applied Mathematical Sciences, vol.7, pp.237-246, (2013) DOI: 10.12988/ams.2013.13022(CrossRef)(Google Scholar)
[20] R. Rameshbabu and R. Karthikeyan, “Adaptive synchronization of novel chaotic system and its FPGA implementation,” IEEE Int.conf. on Smart Technologies and Management for Computing, Communication, Controls, Energy and Materials, pp.517-522, (2015) DOI: 10.1109/icstm.2015.7225459 (CrossRef)(Google Scholar)
[21] R. Karthikeyan, A. Prasina, Ramesh Babu, S. Raghavendran, “ Indian Journal of Science and Technology, vol.8, no.11, pp.47901, (2015) DOI: 10.17485/ijst/2015/v8i11/71775(CrossRef)(Google Scholar)
[22] J. Humberto Pérez-Cruz, Pedro A. Tamayo-Meza, Maricela Figueroa, Ramón Silva-Ortigoza, Mario Ponce-Silva, R. Rivera-Blas, and Mario Aldape-Pérez, “Exponential synchronization of chaotic Xian system using linear feedback control,” Complexity, vol.2019, Article ID 4706491, (2019) DOI: 10.1155/2019/4706491 (CrossRef)(Google Scholar)
[23] F. Hannachi, “Analysis, dynamics and adaptive control synchronization of a novel chaotic 3-D system,” SN Applied Sciences,” vol.1, no.158, (2019) DOI: 10.1007/s42452-019-0175-3(CrossRef)(Google Scholar)
[24] A. Khan, M. Budhraja, and A. Ibraheem, “Synchronization among different switches of four non identical chaotic system via adaptive control,” Arabian Journal for Science and Engineering, vol.44, pp.2717-2728 (2019) DOI: 10.1007/s13369-018-3458-x(CrossRef)(Google Scholar)
[25] S. Vaidyanathan, O. Abba, B. Gambo, and M. Alidou, “A new three dimensional chaotic system: its adaptive control and circuit design,” International Journal of Automation and Control, vol.13, no.1, pp.101 - 121 (2019) DOI: 10.1504/ijaac.2019.10016561 (CrossRef)(Google Scholar)
[26] L. Kocarev and U. Partliz, “General Approach for Chaotic Synchronization with Applications to Communications,” Physical Review Letters vol.74, pp.5028-5030, (1995) DOI: 10.1103/physrevlett.74.5028 (CrossRef)(Google Scholar)
[27] J. Lu and X. Wu, “Synchronization of a Unified Chaotic System and the Application in Secure Communication,” Physics Letter A Vol. 305, pp.365 (2002) DOI: 10.1016/s0375-9601(02)01497-4 (CrossRef)(Google Scholar)
[28] E. Ott, C. Grebogi, and J.A Yorke, “Controlling chaos,” Phys. Review Letters, vol.64, pp.1196-1199, (1990) DOI: /10.1103/physrevlett.64.1196 (CrossRef)(Google Scholar)
[29] Ho and Hung, “Synchronization of two different chaotic systems using generalized active control,” Phys Rev Letter A. vol.301, pp.424-8, (2002) DOI: 10.1515/ijnsns.2005.6.3.249 (CrossRef)(Google Scholar)
[30] M.T. Yassen, “Chaos synchronization between two different chaotic systems using active control,” Chaos, Solitons Fractals, Vol. 23, pp.131-140, (2005) DOI: 10.1016/j.chaos.2004.03.038 (CrossRef)(Google Scholar)
[31] V. Sundarapandian and R. Karthikeyan, “Active controller design for global chaos anti synchronization of Li and Tigan chaotic systems,” International Journal of Information Technology and Computer Science, vol.3, pp.255-268, (2011) DOI: 10.5121/ijcsit.2011.3420 (CrossRef)(Google Scholar)
[32] T. Hamed, “On complete control and synchronization of Zhang chaotic system with uncertain parameters using adaptive control method,” Nonlinear Engineering, vol.2017, pp.7, pp.45-50, (2017) DOI: 10.1515/nleng-2017-0050(CrossRef)(Google Scholar)
[33] K. Ajith, K. Vijay, and Subir Das, “Synchronization of Time delay chaotic systems with uncertainties and external disturbances,” Discontinuity, Nonlinearity, and Complexity, vol.8, pp.13-21, (2019) DOI: 10.5890/dnc.2019.03.002 (CrossRef)(Google Scholar)
[34] F.F. Cun, R.T. Yan, H.W. Ying, and Y.Y. Hai, “Active backstepping control of projective synchronization among different non-linear systems,” Journal of Control, Measurements, Electronics, computing and communications, vol.58, pp.295-301, (2019) DOI: 10.1080/00051144.2018.1432466(CrossRef)(Google Scholar)
[35] S.F. Jiunn, H.T. Jason Sheng, J.Y. Jun, and M.G. Shu, “Adaptive chattering free sliding mode control of chaotic systems with unknown input nonlinearity via smooth hyperbolic tangent function,” Mathematical Problems in Engineering, vol.2019, pp.9, (2019) DOI: 10.1155/2019/4509674 (CrossRef)(Google Scholar)
[36] E. Deniz, P. Tiago, and S.W. Jereon, “Synchronization of chaos and its applications,” Contemporary Physics, vol.58, pp.207 - 243, (2017) DOI: 10.1080/00107514.2017.1345844(CrossRef)(Google Scholar)
[37] L. Chen, C. Huang, H. Liu, and Y. Xia, “Anti synchronization of a class of chaotic systems with applications to Lorenz system: A unified analysis of integer order and Fractional order,” Mathematics, vol.7, pp.559, (2019) DOI: 10.3390/math7060559 (CrossRef)(Google Scholar)
[38] X. Chai and Z. Huigan, “Function projective lag synchronization of chaotic systems with certain parameters via adaptive - impulsive control,” International Journal of Automation and computing, vol.16, pp.238-247, (2019) DOI: 10.1007/s11633-016-1020-4(CrossRef)(Google Scholar)
[39] S. Vaidyanathan, A. Sambas, S. Kacar, and U. Cavusoglu, “A new finance chaotic system, its electronic realization, passivity based synchronization, and an application to voice encryption,” Nonlinear Engineering, vol.8, pp.193 - 205, (2019) DOI:10.1515/nleng-2018-0012(CrossRef)(Google Scholar)