{"references": ["R. May, \"Simple mathematical models with very complicated dynamics,\" Nature, vol. 261, pp. 459\u2013467, 1976, doi: 10.1038/261459A0", "C. Wang, N. Jiang, G. Li, C. Xue, A. Zhao and K. Qiu, \"Secure chaotic communication with spectrum expansion/compression,\" 2017 16th International Conference on Optical Communications and Networks (ICOCN), 2017, pp. 1-3, doi: 10.1109/ICOCN.2017.8121333", "G. Tang, L. Zhu, Q. Wu, Q. He and L. Yu, \"A hybrid spread spectrum communication method based on chaotic sequence,\" 2021 International Symposium on Networks, Computers and Communications (ISNCC), 2021, pp. 1-5, doi: 10.1109/ISNCC52172.2021.9615817", "N. X. Quyen, V. Van Yem and T. M. Hoang, \"Chaotic modulation based on the combination of CPPM and CPWM,\" Proceedings of the Joint INDS'11 & ISTET'11, 2011, pp. 1-6, doi: 10.1109/INDS.2011.6024801", "H. Leung, H. Yu, and K. Murali, \"Ergodic chaos-based communication schemes,\" in Phys Rev E Stat Nonlin Soft Matter Phys, vol. 66, no. 3 Pt 2A, 2002, pp. 036203, doi:10.1103/PhysRevE.66.036203", "J. Borwein, and D. Bailey, \"Bifurcation points in the logistic iteration,\" in Mathematics by Experiment: Plausible Reasoning in the 21st Century, Wellesley, MA: A K Peters, pp. 50-53, 2003", "H. N. Abdullah and I. F. Ali, \"Design of chaotic bifurcation parameter modulation scheme using mean value estimation,\" Iraqi Journal of ICT, vol. 1, no. 1, pp. 52\u201361, May 2018, doi: 10.31987/ijict.1.1.13", "T. Tsuchiya and D. Yamagishi, \"The complete bifurcation diagram for the logistic map,\" Zeitschrift f\u00fcr Naturforschung A, vol. 52, no. 6-7, 1997, pp. 513-516, doi: 10.1515/zna-1997-6-708", "M. M. de A. Kotaki and M. Luppe, \"FPGA implementation of a pseudorandom number generator based on k \u2013 logistic map,\" 2020 IEEE 11th Latin American Symposium on Circuits & Systems (LASCAS), 2020, pp. 1-4, doi: 10.1109/LASCAS45839.2020.9068999", "Z. Mu and H. Liu, \"Research on digital media image encryption algorithm based on Logistic chaotic map,\" 2020 International Conference on Robots & Intelligent System (ICRIS), 2020, pp. 108-111, doi: 10.1109/ICRIS52159.2020.00035", "S. Hayes, C. Grebogi, E. Ott, \"Communicating with chaos,\" Phys Rev Lett, vol. 70, no. 20, 1993, pp. 3031-3034, doi:10.1103/PhysRevLett.70.3031", "A. Riaz and M. Ali, \"Chaotic communications, their applications and advantages over traditional methods of communication,\" 2008 6th International Symposium on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 21-24, doi: 10.1109/CSNDSP.2008.4610808", "Z. Xing, \"Chaotic wireless communication and related network information security inversion technology,\" 2020 International Conference on Advance in Ambient Computing and Intelligence (ICAACI), 2020, pp. 36-41, doi: 10.1109/ICAACI50733.2020.00012", "M. Xu, Y. Song and L. Liu, \"A novel demodulation method for chaotic parameter modulation,\" 2006 International Conference on Wireless Communications, Networking and Mobile Computing, 2006, pp. 1-4, doi: 10.1109/WiCOM.2006.156", "H. Jin-feng and G. Jing-bo, \"A novel UPF-based demodulator for chaotic parameter modulation systems,\" 2007 2nd IEEE Conference on Industrial Electronics and Applications, 2007, pp. 2575-2578, doi: 10.1109/ICIEA.2007.4318878", "M. Kozlenko and V. Vialkova, \"Software defined demodulation of multiple frequency shift keying with dense neural network for weak signal communications,\" 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), 2020, pp. 590-595, doi: 10.1109/TCSET49122.2020.235501", "I. Lazarovych et al., \"Software implemented enhanced efficiency BPSK demodulator based on perceptron model with randomization,\" 2021 IEEE 3rd Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2021, pp. 221-225, doi: 10.1109/UKRCON53503.2021.9575458", "M. Kozlenko, I. Lazarovych, V. Tkachuk, and V. Vialkova, \"Software demodulation of weak radio signals using convolutional neural network,\" 2020 IEEE 7th International Conference on Energy Smart Systems (ESS), 2020, pp. 339-342, doi: 10.1109/ESS50319.2020.9160035", "C. Li, F. Marzani, and F. Yang, \"Demodulation of chaos phase modulation spread spectrum signals using machine learning methods and its evaluation for underwater acoustic communication,\" Sensors, vol. 18, no. 12, p. 4217, Dec. 2018, doi: 10.3390/s18124217", "G. \u00c1lvarez, F. Montoya, M. Romera, and G. Pastor, \"Breaking parameter modulated chaotic secure communication system,\" Chaos, Solitons & Fractals, vol. 21, no. 4, 2004, pp. 783-787, doi: 10.1016/j.chaos.2003.12.041", "Hai-Peng Ren, Hui-Ping Yin, Hong-Er Zhao, C. Bai, C. Grebogi, \"Artificial intelligence enhances the performance of chaotic baseband wireless communication,\" IET Communication, vol. 15, 2021, pp. 1467\u20131479, doi: 10.1049/cmu2.12162", "Wolfram MathWorld, \"Logistic map,\" Wolfram MathWorld. [Online]. Available: https://mathworld.wolfram.com/LogisticMap.html [Accessed Nov. 28, 2022]"]}

A chaotic modulation scheme is an efficient wideband communication method. It utilizes the deterministic chaos to generate pseudo-random carriers. Chaotic bifurcation parameter modulation is one of the well-known and widely-used techniques. This paper presents the machine learning based demodulation approach for the bifurcation parameter keying. It presents the structure of a convolutional neural network as well as performance metrics values for signals generated with the chaotic logistic map. The paper provides an assessment of the overall accuracy for binary signals. It reports the accuracy value of 0.88 for the bifurcation parameter deviation of 1.34% in the presence of additive white Gaussian noise at the normalized signal-to-noise ratio value of 20 dB for balanced dataset.

M. Kozlenko, "Supervised machine learning based signal demodulation in chaotic communications," 2022 International Conference on Innovative Solutions in Software Engineering (ICISSE), Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine, Nov. 29-30, 2022, pp. 313-317, doi: 10.5281/zenodo.7512427