Transformation of the generalized chaotic system into the discrete-time complex domain
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A. J. Menezes, P. C. Van Oorschot, and S. A. Vanstone, "Handbook of Applied Cryptography CRC Press," Boca Rat., 1997, [Online]. Available: Google Scholar.
C. E. Shannon, "Claude Elwood Shannon: Collected Papers," 1993, [Online]. Available: https://dl.acm.org/doi/book/10.5555/174843.
C. E. Shannon, "A Mathematical Theory of Communication," Bell Syst. Tech. J., vol. 27, no. 3, pp. 379–423, Jul. 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x.
G. A. Jones and J. Mary Jones, "Information and Coding Theory," 2000, doi: 10.1007/978-1-4471-0361-5.
D. Coppersmith, "The Data Encryption Standard (DES) and its strength against attacks," IBM J. Res. Dev., vol. 38, no. 3, pp. 243–250, May 1994, doi: 10.1147/rd.383.0243.
M. W. Hirsch, S. Smale, and R. L. Devaney, "Differential Equations, Dynamical Systems, and an Introduction to Chaos," 2013, doi: 10.1016/C2009-0-61160-0.
G. C. Layek, "An Introduction to Dynamical Systems and Chaos," 2015, doi: 10.1007/978-81-322-2556-0.
N. Swarupa, "Design and Simulation of Chaotic Colpitt's Oscillator," 2018 Second Int. Conf. Electron. Commun. Aerosp. Technol., pp. 1505–1508, Mar. 2018, doi: 10.1109/ICECA.2018.8474857.
C. Wannaboon and T. Masayoshi, "An autonomous chaotic oscillator based on hyperbolic tangent nonlinearity," 2015 15th Int. Symp. Commun. Inf. Technol., pp. 323–326, Oct. 2015, doi: 10.1109/ISCIT.2015.7458372.
T. Xie, X. Wei, and R. Yu, "Noise Immunity Analysis in External Excitation Chaotic Oscillator Detecting System," 2010 Int. Conf. Intell. Syst. Des. Eng. Appl., pp. 1013–1016, Oct. 2010, doi: 10.1109/ISDEA.2010.154.
E. V Efremova, A. Y. Nikishov, and A. I. Panas, "UWB microwave chaotic oscillator: From distributed structure to CMOS IC realization," Proc. Pap. 5th Eur. Conf. Circuits Syst. Commun., pp. 67–70, 2010, [Online]. Available: https://ieeexplore.ieee.org/abstract/document/5733858.
S. Hu, S. Yu, Y. Hu, Z. Wang, and B. Zhou, "A Novel 1–6 GHz Chaotic Signal Oscillator for Broadband Communication Systems," 2018 Prog. Electromagn. Res. Symp., pp. 1550–1554, Aug. 2018, doi: 10.23919/PIERS.2018.8598177.
A. Semenov, O. Osadchuk, O. Semenova, O. Bisikalo, O. Vasilevskyi, and O. Voznyak, "Signal Statistic and Informational Parameters of Deterministic Chaos Transistor Oscillators for Infocommunication Systems," 2018 Int. Sci. Conf. Probl. Infocommunications. Sci. Technol. (PIC S&T), pp. 730–734, Oct. 2018, doi: 10.1109/INFOCOMMST.2018.8632046.
S. Ergun, "Cryptanalysis of a random number generator based on a double-scroll chaotic oscillator," 2016 Int. Symp. Intell. Signal Process. Commun. Syst., pp. 1–4, Oct. 2016, doi: 10.1109/ISPACS.2016.7824723.
M. Moundher, B. Hichem, T. Djamel, and S. Said, "Novel Four-dimensional Chaotic Oscillator for Sub-1GHz Chaos-Based Communication Systems," 2019 6th Int. Conf. Image Signal Process. their Appl., pp. 1–5, Nov. 2019, doi: 10.1109/ISPA48434.2019.8966791.
K. Klomkarn and P. Sooraksa, "A Universal-Mode Chaotic Oscillator," 2019 Jt. Int. Conf. Digit. Arts, Media Technol. with ECTI North. Sect. Conf. Electr. Electron. Comput. Telecommun. Eng. (ECTI DAMT-NCON), pp. 314–317, Jan. 2019, doi: 10.1109/ECTI-NCON.2019.8692295.
M. Tabatabaei, J. Zarei, R. Razavi-Far, and M. Saif, "Secure Communication Based on Fractional Chaotic System by a Novel Robust Filter Algorithm," 2020 IEEE Int. Syst. Conf., pp. 1–6, Aug. 2020, doi: 10.1109/SysCon47679.2020.9275914.
J. Kim, B. Van Nguyen, H. Jung, J.-H. Lee, and K. Kim, "A Novel Chaotic Time Hopping TH-NRDCSK System for Anti-jamming Communications," 2019 IEEE Wirel. Commun. Netw. Conf., pp. 1–3, Apr. 2019, doi: 10.1109/WCNC.2019.8885532.
S. A. R. F. M. Nejad and A. Sahab, "A novel 5-D hyper-chaotic system with single equilibrium point and designing a controller for it using the optimal generalized back-stepping method," 2017 IEEE Int. Conf. Cybern. Comput. Intell., pp. 29–33, Nov. 2017, doi: 10.1109/CYBERNETICSCOM.2017.8311710.
L.-M. Tam and S.-Y. Li, "Novel-fuzzy-model based modeling and control of nonlinear chaotic systems with uncertainty," 2015 Int. Conf. Adv. Robot. Intell. Syst., pp. 1–6, May 2015, doi: 10.1109/ARIS.2015.7158361.
H. Deng, T. Li, Q. Wang, and H. Li, "A Novel Chaotic Slow FH System Based on Differential Space-Time Modulation," 2008 Int. Conf. Embed. Softw. Syst. Symp., pp. 380–385, Jul. 2008, doi: 10.1109/ICESS.Symposia.2008.71.
R. Voliansky, O. Kluev, O. Sadovoi, O. Sinkevych, and N. Volianska, "Chaotic Time-variant Dynamical System," 2020 IEEE 15th Int. Conf. Adv. Trends Radioelectron. Telecommun. Comput. Eng., pp. 606–609, Feb. 2020, doi: 10.1109/TCSET49122.2020.235503.
R. Voliansky, A. Pranolo, A. P. Wibawa, and Haviluddin, "Transformation of 3-D Jerk Chaotic System into Parallel Form," 2018 Int. Symp. Adv. Intell. Informatics, pp. 179–184, Aug. 2018, doi: 10.1109/SAIN.2018.8673346.
H. Chen, L. Wu, L.-D. Lin, G.-Q. Lan, and Q. Ding, "Simulation Experiment Research on the Chaotic Characteristics of the Simple Unary Polynomial Transformation," 2012 Fifth Int. Work. Chaos-fractals Theor. Appl., pp. 118–122, Oct. 2012, doi: 10.1109/IWCFTA.2012.34.
Z. Zhu, S. Li, H. Yu, X. Liu, and J. Song, "An approach of chaotic generalized synchronization with the space transformation," 2008 IEEE Int. Symp. Ind. Electron., pp. 1088–1092, Jun. 2008, doi: 10.1109/ISIE.2008.4676930.
H. Chen, M. Gao, and H. Zhang, "Study Chaotic Sequences by Unary Quadratic Nonlinear Transformation," 2011 Fourth Int. Work. Chaos-Fractals Theor. Appl., pp. 169–173, Oct. 2011, doi: 10.1109/IWCFTA.2011.17.
R. Voliansky, O. Sadovoi, Y. Shramko, N. Volianska, and O. Sinkevych, "Arduino-based Implementation of the Dual-channel Chaotic Generator," 2019 3rd Int. Conf. Adv. Inf. Commun. Technol., pp. 278–281, Jul. 2019, doi: 10.1109/AIACT.2019.8847904.
M. Jalilian, A. Ahmadi, and M. Ahmadi, "Hardware Implementation of A Chaotic Pseudo Random Number Generator Based on 3D Chaotic System without Equilibrium," 2018 25th IEEE Int. Conf. Electron. Circuits Syst., pp. 741–744, Dec. 2018, doi: 10.1109/ICECS.2018.8617960.
H. Zheng, S. Yu, and J. Lu, "Multi-images chaotic communication and FPGA implementation," Proc. 33rd Chinese Control Conf., pp. 5481–5485, Jul. 2014, doi: 10.1109/ChiCC.2014.6895876.
S. Liu, "Research on the design and implementation of two dimensional hyper chaotic sequence cipher algorithm," 2017 Sixth Int. Conf. Futur. Gener. Commun. Technol., pp. 1–4, Aug. 2017, doi: 10.1109/FGCT.2017.8103730.
S. Liu, "Research on the Design and Implementation of Two Dimensional Hyper Chaotic Sequence Cipher Algorithm," 2017 Int. Conf. Comput. Syst. Electron. Control, pp. 1185–1187, Dec. 2017, doi: 10.1109/ICCSEC.2017.8446935.
E. Huesca and S. Mondie, "Lyapunov matrix of linear systems with delays: A polynomial approximation," 2009 6th Int. Conf. Electr. Eng. Comput. Sci. Autom. Control, pp. 1–6, Nov. 2009, doi: 10.1109/ICEEE.2009.5393438.
A. Krifa and K. Bouzrara, "Approximation of nonlinear term in model robotic," 2017 Int. Conf. Control. Autom. Diagnosis, pp. 185–190, Jan. 2017, doi: 10.1109/CADIAG.2017.8075654.
D. Babic, "Piecewise polynomial approximation based on taylor series with efficient realization using Farrow structure," 2009 9th Int. Conf. Telecommun. Mod. Satell. Cable, Broadcast. Serv., pp. 241–244, Oct. 2009, doi: 10.1109/TELSKS.2009.5339415.
C. Lubich, D. Mansour, and C. Venkataraman, "Backward difference time discretization of parabolic differential equations on evolving surfaces," IMA J. Numer. Anal., vol. 33, no. 4, pp. 1365–1385, Oct. 2013, doi: 10.1093/imanum/drs044.
K. B. Janiszowski, "A modification and the Tustin approximation," IEEE Trans. Automat. Contr., vol. 38, no. 8, pp. 1313–1316, 1993, doi: 10.1109/9.233177.
Jang-Ho Seo, Chang-Hwan Im, Chang-Geun Heo, Jae-Kwang Kim, Hyun-Kyo Jung, and Cheol-Gyun Lee, "Multimodal function optimization based on particle swarm optimization," IEEE Trans. Magn., vol. 42, no. 4, pp. 1095–1098, Apr. 2006, doi: 10.1109/TMAG.2006.871568.
P. Amil, C. Cabeza, and A. C. Marti, "Exact Discrete-Time Implementation of the Mackey–Glass Delayed Model," IEEE Trans. Circuits Syst. II Express Briefs, vol. 62, no. 7, pp. 681–685, Jul. 2015, doi: 10.1109/TCSII.2015.2415651.
DOI: http://dx.doi.org/10.26555/jifo.v15i1.a20222
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