• Pham Duc Hung Hung Yen University of Technology and Education
  • Huynh Tuan Tu Lac Hong University, Bien Hoa
  • Nguyen Viet Ngu Hung Yen University of Technology and Education
  • Le Thi Minh Tam Hung Yen University of Technology and Education
Keywords: Fuzzy inference system, brain emotional learning controller, cerebellar model articulation controller, 4-D Lorentz-Stenflo chaotic system


This study poses a new efficient control system based on two types of networks that are a fuzzy brain emotional learning control (BELC) network and fuzzy cerebellar model articulation control (CMAC) network. The proposed control system, FBCC (fuzzy BELC and fuzzy CMAC), has the advantages of fuzzy inference systems, the ability of making decision, and the emotional activity. In order to demonstrate the effectiveness of the proposed control method, the simulation results of a 4-dimensional (4D) Lorentz-Stenflo chaotic system is used, and a comparison between the proposed FBCC and other controllers shows that the proposed control system achieves better control performance.


Kaur, Gurvir, Kuldeepak Singh, and Harsimranjit Singh Gill, “Chaos-based joint speech encryption scheme using SHA-1,” Multimedia Tools and Applications, 2021.

Grzybowski, J. M. V., E. E. N. Macau, and T. Yoneyama. “Chaos-Based Communication Using Isochronal Synchronization: Considerations About the Synchronization Manifold.” Nonlinear Dynamics, Chaos, and Complexity. Springer, Singapore, pp. 75-94, 2021.

Kekha Javan, Ali Akbar, et al., “Design of Adaptive-Robust Controller for Multi-State Synchronization of Chaotic Systems with Unknown and Time-Varying Delays and Its Application in Secure Communication,” Sensors, vol 21(1), pp. 254-275, 2021.

Khan, Ayub, Lone Seth Jahanzaib, and Pushali Trikha. “Changing Dynamics of the First, Second and Third Approximations of the Exponential Chaotic System and Their Application in Secure Communication Using Synchronization.” International Journal of Applied and Computational Mathematics 7.1, 2021.

M. P. Shareef and T. V. Divya, “Secret audio watermarking using empirical mode decomposition and chaotic map,” 2015 International Conference on Power, Instrumentation, Control and Computing (PICC), Thrissur, pp. 1-5, 2015.

Y. Wang, Z. Li and J. Sun, “Three-Variable Chaotic Oscillatory System Based on DNA Strand Displacement and Its Coupling Combination Synchronization,” in IEEE Transactions on NanoBioscience, vol. 19, no. 3, pp. 434-445, 2020.

Takhi, H., Kemih, K., Moysis, L., & Volos, C. Passivity based sliding mode control and synchronization of a perturbed uncertain unified chaotic system. Mathematics and Computers in Simulation, 181, pp. 150-169, 2021.

Ma, Xin, Yeguo Sun, and Fang Zhu., “Nonsingular Terminal Sliding Mode Control of Uncertain Chaotic Gyroscope System Based on Disturbance Observer,” Journal of Mathematics, 2021.

Farid, Y., & Ramezani, A., “A Wavelet-Based Robust Adaptive TS Fuzzy Controller Design for Synchronization of Faulty Chaotic Gyrostat Systems,” Journal of Control, Automation and Electrical Systems, 32(1), pp. 57-69, 2021.

Huynh T.-T., Le T. L, and Lin C. M., “Self-organizing recurrent wavelet fuzzy neural network-based control system design for MIMO uncertain nonlinear systems using TOPSIS method.” International Journal of Fuzzy Systems, vol. 21, no. 2, pp. 468-487, 2019.

Yu, Nanxiang, and Wei Zhu, “Event-triggered impulsive chaotic synchronization of fractional-order differential systems,” Applied Mathematics and Computation, 388, 2021.

Zhang, Ying, Yong He, and Fei Long, “Augmented two-side-looped Lyapunov functional for sampled-data-based synchronization of chaotic neural networks with actuator saturation,” Neurocomputing, 422, 2021.

Lin, C.M and Huynh, T.T, “Synchronization of Nonlinear Chaotic Systems Using Modified Function-Link Fuzzy Cerebellar Model Articulation Controller,” 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), Bari, Italy, pp. 915-920, 2019.

Lin, Chih-Min, Ya-Fu Peng, and Ming-Hung Lin. “CMAC-based adaptive backstepping synchronization of uncertain chaotic systems.” Chaos, Solitons & Fractals 42.2, pp 981-988, 2009.

Huynh, Tuan-Tu, Chih-Min Lin, and Tien-Loc Le. “A Double Function-Link Function-Based Fuzzy Brain Emotional Controller for Synchronizing a 4D Hyper-Chaotic System,” 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2020.

Lin, Chih-Min, and Chang-Chih Chung. “Fuzzy brain emotional learning control system design for nonlinear systems,” International Journal of Fuzzy Systems, Vol. 17, no.2, pp 117-128, 2015.

Huynh T.-T., Lin C.-M., Le T.-L., Nguyen N. P., Hong S.-K., and Chao F., “Wavelet interval type-2 fuzzy quad-function-link brain emotional control algorithm for the synchronization of 3D nonlinear chaotic systems,” International Journal of Fuzzy Systems, 22 (8), pp. 2546-2564, 2020.

Yang, CC., “Adaptive Single Input Control for Synchronization of a 4D Lorenz–Stenflo Chaotic System,” Arab J Sci Eng, 39, pp. 2413–2426, 2014.

How to Cite
Pham Duc Hung, Huynh Tuan Tu, Nguyen Viet Ngu, & Le Thi Minh Tam. (2021). CHAOS SYNCHRONIZATION USING FUZZY BRAIN EMOTIONAL LEARNING CONTROLLERS. UTEHY Journal of Science and Technology, 28, 54-60. Retrieved from