Abstract
This paper is concerned with the synchronization of hyperchaotic Wang-Liu system by using the Pecora-Carroll complete replacement method. One of the most important features of this method is no need for a controller on the slave system which is the basic requirement of other synchronization methods. Initially in this study, dynamic analyses are given to describe the structure of the system. Then, the synchronization is investigated and master and slave systems that have two different dynamics are synchronized. At this point, the hyperchaotic master system forces the quasi-periodic slave system to behave as itself and they demonstrate the same hyperchaotic dynamics after a while. Besides the simulations, synchronization of the two systems is also verified by the experimental realization. FPAA and FPGA implementations of hyperchaos synchronization are provided and results are considered. In the end, it is specified that the experimental results are well-coincides with the simulations.
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References
Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Science, 20(2), 130–141. https://doi.org/10.1175/1520-0469(1963)020%3c0130:dnf%3e2.0.co;2
Rossler, O. E. (1979). An equation for hyperchaos. Physics Letters A. https://doi.org/10.1016/0375-9601(79)90150-6
Chua, L. O., & Kobayashi, K. (1986). Hyperchaos: Laboratory experiment and numerical confirmation. IEEE Transactions on Circuits and Systems, 33(11), 1143–1147. https://doi.org/10.1109/TCS.1986.1085862
Wang, X., & Wang, M. (2008). A hyperchaos generated from Lorenz system. Physica A: Statistical Mechanics and its Applications, 387(14), 3751–3758. https://doi.org/10.1016/j.physa.2008.02.020
Wang, F. Q., & Liu, C. X. (2006). Hyperchaos evolved from the Liu chaotic system. Chinese Physics, 15(5), 963–968. https://doi.org/10.1088/1009-1963/15/5/016
Gao, T., Chen, Z., Yuan, Z., & Chen, G. (2006). A hyperchaos generated from Chen’s system. International Journal of Modern Physics C, 17(4), 471–478. https://doi.org/10.1142/S0129183106008625
Vaidyanathan, S., Dolvis, L. G., Jacques, K., Lien, C. H., & Sambas, A. (2019). A new five-dimensional four-wing hyperchaotic system with hidden attractor, its electronic circuit realisation and synchronisation via integral sliding mode control. International Journal of Modelling, Identification and Control, 32(1), 30–45. https://doi.org/10.1504/IJMIC.2019.101959
Yujun, N., Xingyuan, W., Mingjun, W., & Huaguang, Z. (2010). A new hyperchaotic system and its circuit implementation. Communications in Nonlinear Science and Numerical Simulation, 15(11), 3518–3524. https://doi.org/10.1016/j.cnsns.2009.12.005
Brahim, A. H., Pacha, A. A., & Said, N. H. (2021). A new image encryption scheme based on a hyperchaotic system & multi specific S-boxes. The International Journal of Information Security. https://doi.org/10.1080/19393555.2021.1943572
Chen, X., et al. (2020). Pseudorandom number generator based on three kinds of four-wing memristive hyperchaotic system and its application in image encryption. Complexity. https://doi.org/10.1155/2020/8274685
Setoudeh, F., & Sedigh, A. K. (2021). Nonlinear analysis and minimum L2-norm control in memcapacitor-based hyperchaotic system via online particle swarm optimization. Chaos, Solitons & Fractals, 151, 111214. https://doi.org/10.1016/J.CHAOS.2021.111214
Xiu, C., Zhou, R., Zhao, S., & Xu, G. (2021). Memristive hyperchaos secure communication based on sliding mode control. Nonlinear Dynamics. https://doi.org/10.1007/s11071-021-06302-9
Chen, Y., Zhang, H., & Kong, X. (2021). A new fractional-order hyperchaotic system and its adaptive tracking control. Discrete Dynamics in Nature and Society. https://doi.org/10.1155/2021/6625765
Hui, Y., Liu, H., & Fang, P. (2021). A DNA image encryption based on a new hyperchaotic system. Multimedia Tools and Applications. https://doi.org/10.1007/s11042-021-10526-7
Wang, X., & Zhao, M. (2021). An image encryption algorithm based on hyperchaotic system and DNA coding. Optics & Laser Technology, 143, 107316. https://doi.org/10.1016/J.OPTLASTEC.2021.107316
Zhou, Y., Bi, M., Zhuo, X., Lv, Y., Yang, X., & Hu, W. (2021). Physical layer dynamic key encryption in OFDM-PON system based on cellular neural network. IEEE Photonics Journal. https://doi.org/10.1109/JPHOT.2021.3059369
Luo, J., Qu, S., Chen, Y., Chen, X., & Xiong, Z. (2021). Synchronization, circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller. Chinese Journal of Physics, 71, 403–417. https://doi.org/10.1016/j.cjph.2021.03.009
Bian, Y., & Yu, W. (2021). A secure communication method based on 6-D hyperchaos and circuit implementation. Telecommunication Systems, 77, 73. https://doi.org/10.1007/s11235-021-00790-1
Yu, W., et al. (2019). Design of a new seven-dimensional hyperchaotic circuit and its application in secure communication. IEEE Access, 7, 125586–125608. https://doi.org/10.1109/ACCESS.2019.2935751
Benkouider, K., Bouden, T., Yalcin, M. E., & Vaidyanathan, S. (2020). A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design. International Journal of Modelling, Identification and Control, 35(3), 241–257. https://doi.org/10.1504/IJMIC.2020.114191
Singh, S., Han, S., & Lee, S. M. (2021). Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems. Journal of the Franklin Institute. https://doi.org/10.1016/J.JFRANKLIN.2021.07.037
Vaidyanathan, S., & Rasappan, S. (2011). Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Communications in Computer and Information Science, 198, 10–17. https://doi.org/10.1007/978-3-642-22555-0_2
Pecora, L. M., & Carroll, T. L. (1990). Synchronization in Chaotic systems.
Lai, Q., Wan, Z., Kuate, P. D. K., & Fotsin, H. (2021). Dynamical analysis, circuit implementation and synchronization of a new memristive hyperchaotic system with coexisting attractors. Modern Physics Letters B. https://doi.org/10.1142/S0217984921501876
Sajjadi, S. S., Baleanu, D., Jajarmi, A., & Pirouz, H. M. (2020). A new adaptive synchronization and hyperchaos control of a biological snap oscillator. Chaos Solitons and Fractals. https://doi.org/10.1016/j.chaos.2020.109919
Vaidyanathan, S., Pham, V. T., Volos, C., & Sambas, A. (2018). A novel 4-D hyperchaotic rikitake dynamo system with hidden attractor, its properties, synchronization and circuit design. In Studies in systems, decision and control (Vol. 133, pp. 345–364). Berlin: Springer.
Liao, T. L., Wan, P. Y., & Yan, J. J. (2022). Design and synchronization of chaos-based true random number generators and its FPGA implementation. IEEE Access. https://doi.org/10.1109/ACCESS.2022.3142536
Wang, P., Wen, G., Yu, X., Yu, W., & Huang, T. (2019). Synchronization of multi-layer networks: From node-to-node synchronization to complete synchronization. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(3), 1141–1152. https://doi.org/10.1109/TCSI.2018.2877414
Al-Obeidi, A. S., & Al-Azzawi, S. F. (2019). Projective synchronization for a cass of 6-D hyperchaotic lorenz system. Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 692–700. https://doi.org/10.11591/IJEECS.V16.I2.PP692-700
Wu, X., Fu, Z., & Kurths, J. (2015). A secure communication scheme based generalized function projective synchronization of a new 5D hyperchaotic system. Physica Scripta. https://doi.org/10.1088/0031-8949/90/4/045210
Gularte, K. H. M., Alves, L. M., Vargas, J. A. R., Alfaro, S. C. A., De Carvalho, G. C., & Romero, J. F. A. (2021). Secure communication based on hyperchaotic underactuated projective synchronization. IEEE Access, 9, 166117–166128. https://doi.org/10.1109/ACCESS.2021.3134829
Zhou, C., Yang, C., Xu, D., & Chen, C. Y. (2019). Dynamic analysis and finite-time synchronization of a new hyperchaotic system with coexisting attractors. IEEE Access, 7, 52896–52902. https://doi.org/10.1109/ACCESS.2019.2911486
Sangpet, T., & Kuntanapreeda, S. (2020). Finite-time synchronization of hyperchaotic systems based on feedback passivation. Chaos, Solitons & Fractals, 132, 109605. https://doi.org/10.1016/J.CHAOS.2020.109605
Al-Obeidi, A. S., Al-Azzawi, S. F., Hamad, A. A., Thivagar, M. L., Meraf, Z., & Ahmad, S. (2021). A novel of new 7D Hyperchaotic system with self-excited attractors and its hybrid synchronization. Computational Intelligence and Neuroscience. https://doi.org/10.1155/2021/3081345
Sarasu, P., & Sundarapandian, V. (2011). The generalized projective synchronization of hyperchaotic lorenz and hyperchaotic Qi systems via active control. International Journal of Soft Computing, 6(5), 216–223. https://doi.org/10.3923/IJSCOMP.2011.216.223
Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997). Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos, 7(4), 520–543. https://doi.org/10.1063/1.166278
Wang, F., Wang, R., Iu, H. H. C., Liu, C., & Fernando, T. (2019). A novel multi-shape chaotic attractor and its FPGA implementation. IEEE Transactions on Circuits and Systems II: Express Briefs, 66(12), 2062–2066. https://doi.org/10.1109/TCSII.2019.2907709
Kiliç, R., Alçi, M., & Günay, E. (2004). A SC-CNN-based chaotic masking system with feedback. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 14(1), 245–256. https://doi.org/10.1142/S0218127404009120
Günay, E., & Altun, K. (2018). Lorenz-like system design using cellular neural networks. Turkish Journal of Electrical Engineering and Computer Science, 26(4), 1812–1819. https://doi.org/10.3906/elk-1706-309
Salih, T. A. (2021). Design and implementation of a low power consumption of ASK, FSK PSK, and QSK Modulators based on FPAA technology. International Journal on Advanced Science, Engineering and Information Technology, 11(4), 1288. https://doi.org/10.18517/ijaseit.11.4.11299
Diab, M. S., & Mahmoud, S. A. (2020). Field programmable analog arrays for implementation of generalized nth-order operational transconductance amplifier-C elliptic filters. ETRI Journal, 42(4), 534–548. https://doi.org/10.4218/ETRIJ.2020-0104
Vaidyanathan, S., et al. (2021). A 5-D multi-stable hyperchaotic two-disk dynamo system with no equilibrium point: Circuit design, FPGA realization and applications to TRNGs and image encryption. IEEE Access, 9, 81352–81369. https://doi.org/10.1109/ACCESS.2021.3085483
Yu, F., et al. (2020). Multistability analysis, coexisting multiple attractors, and FPGA implementation of Yu-Wang four-wing chaotic system. Mathematical Problems in Engineering. https://doi.org/10.1155/2020/7530976
Yılmaz, G., & Günay, E. (2021). FPAA Implementation of Wang-Liu system. In 2021 13th international conference on electrical and electronics engineering (ELECO) (pp. 167–171). IEEE. https://doi.org/10.23919/ELECO54474.2021.9677754.
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Yılmaz, G., Altun, K. & Günay, E. Synchronization of hyperchaotic Wang-Liu system with experimental implementation on FPAA and FPGA. Analog Integr Circ Sig Process 113, 145–161 (2022). https://doi.org/10.1007/s10470-022-02073-4
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DOI: https://doi.org/10.1007/s10470-022-02073-4