International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies


:: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies

ISSN 2228-9860
eISSN 1906-9642


Vol.11(12) (2020)


    Fatin Nabila Abd Latiff, Wan Ainun Mior Othman, N. Kumaresan (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, 50603, MALAYSIA).

    Disciplinary: Mathematics, Computer Science (Network/Cyber Security).

    ➤ FullText

    DOI: 10.14456/ITJEMAST.2020.229

    Keywords: Chaotic synchronization; Chaotic Neural Network (CNN); Sliding surface; RSA encryption; Double encryption; Cyber security, Cryptography technology.

    Chaotic Neural Networks (CNNs) has been gaining a lot of attention and have become a hot topic from researchers with good expectation. To resolve the synchronization's problem of delayed integer order recurrent neural networks (IoDRNNASM) and delayed fractional-order recurrent neural networks (FoDRNNASM), an active sliding mode control (ASMC) scheme is introduced. Factional Lyapunov direct methodology (FLDM) is designed and is enforced to ASMC of the systems to keep the stability of the systems. To investigate the characteristics of IoDRNNASM and FoDRNNASM, we tend to enforce the method of numerical simulation by utilizing MATLAB programming to demonstrate the performance and efficiency of the results. Based on this study, the results show that the synchronization between integer-order and fractional-order will significantly occur once the recommended ASMC is introduced. This main result can provide a great advantage within the area of network security of secure communication by implement double encryption by conducting RSA encryption. We do believe that this idea can improve security and provides strong protection in secure communications.

    Paper ID: 11A12D

    Cite this article:

    Latiff, F.N.A., Othman, W.A.M., Kumaresan, N. (2020). SYNCHRONIZATION OF DELAYED INTEGER ORDER AND DELAYED FRACTIONAL ORDER RECURRENT NEURAL NETWORKS SYSTEM WITH ACTIVE SLIDING MODE. International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies, 11(12), 11A12D, 1-15.


    [1] Podlubny I. Fractional Differential Equations: Methods of Their Solution and Some of Their Applications. Academic Press; 1998. 340p.

    [2] Hilfer R. Applications of Fractional Calculus in Physics: Applications of Fractional Calculus in Physics; 2000.

    [3] Muthukumar P, Balasubramaniam P. Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dynamics. 2013;74(4):1169-81.

    [4] Pecora LM, Carroll TL. Synchronization in chaotic systems. Physical Review Letters. 1990;64(8):821-4.

    [5] Banerjee S. Chaos synchronization and cryptography for secure communications: applications for encryption: Information Science Reference; 2011. 570- p.

    [6] Nana B, Woafo P, Domngang S. Chaotic synchronization with experimental application to secure communications. Communications in Nonlinear Science and Numerical Simulation. 2009;14(5):2266-76.

    [7] Luo ACJ. A theory for synchronization of dynamical systems. Communications in Nonlinear Science and Numerical Simulation. 2009;14(5):1901-51.

    [8] Sagar RK, Arif M. Synchronization control of two identical three restricted body problems via active control. New Trends in Mathematical Science. 2018;3(6):137-46.

    [9] Vaidyanathan S, Azar AT. Adaptive control and synchronization of Halvorsen circulant chaotic systems. 337: Springer, Cham; 2016. p. 225-47.

    [10] Stamova I, Stamov G. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers. Neural Networks. 2017;96:22-32.

    [11] Chen D, Zhang R, Sprott JC, Chen H, Ma X. Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2012;22(2):023130.

    [12] Liu H, Hou B, Xiang W. Uncertain Nonlinear Chaotic Gyros Synchronization by Using Adaptive Fuzzy Control. International Journal of Online Engineering. 2013;9(3).

    [13] Jia S, Hu C, Yu J, Jiang H. Asymptotical and adaptive synchronization of Cohen–Grossberg neural networks with heterogeneous proportional delays. Neurocomputing. 2018;275:1449-55.

    [14] Li Y, Li C. Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period. Neurocomputing. 2016;173:1341-7.

    [15] Sun W, Wang S, Wang G, Wu Y. Lag synchronization via pinning control between two coupled networks. Nonlinear Dynamics. 2015;79(4): 2659-66.

    [16] Yang X, Ho DWC. Synchronization of delayed memristive neural networks: Robust analysis approach. IEEE Transactions on Cybernetics. 2016;46(10):3377-87.

    [17] Bai EW, Lonngren KE. Sequential synchronization of two Lorenz systems using active control. Chaos, solitons and fractals. 2000;11(7):1041-4.

    [18] Agrawal SK, Srivastava M, Das S. Synchronization of fractional order chaotic systems using active control method. Chaos, Solitons and Fractals. 2012;45(6):737-52.

    [19] Bhalekar S, Daftardar-Gejji V. Synchronization of different fractional-order chaotic systems using active control. Communications in Nonlinear Science and Numerical Simulation. 2010;15(11):3536-46.

    [20] Agiza HN, Yassen MT. Synchronization of Rossler and Chen chaotic dynamical systems using active control. Physics Letters, Section A: General, Atomic and Solid State Physics. 2001;278(4):191-7.

    [21] Ho MC, Hung YC. Synchronization of two different systems by using generalized active control. Physics Letters, Section A: General, Atomic and Solid State Physics. 2002;301(5-6):424-8.

    [22] Lin JS, Yan JJ, Liao TL. Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity. Chaos, Solitons and Fractals. 2005;24(1):371-81.

    [23] Yau HT. Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos, Solitons and Fractals. 2004;22(2):341-7.

    [24] Zhang H, Ma XK, Liu WZ. Synchronization of chaotic systems with parametric uncertainty using active sliding mode control. Chaos, Solitons and Fractals. 2004; 21(5):1249-57.

    [25] Hu T, He Z, Zhang X, Zhong S. Global synchronization of time-invariant uncertainty fractional-order neural networks with time delay: Neurocomputing; 2019. 45-58 p.

    [26] Yang LX, He WS, Liu XJ. Synchronization between a fractional-order system and an integer order system. Computers and Mathematics with Applications. 2011; 62(12):4708-16.

    [27] Stamova I. Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dynamics. 2014; 77(4):1251-60.

    [28] Li C, Deng W. Remarks on fractional derivatives. Applied Mathematics and Computation. 2007;187(2):777-84.

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