Synchronization for fractional-order neural networks with unbounded delays

Authors

  • Thi-Hong Duong Thai Nguyen University of Sciences, Thai Nguyen, Viet Nam
  • Thu-Loan Vu-Thi Thai Nguyen University of Agriculture and Forestry, Thai Nguyen, Viet Nam

DOI:

https://doi.org/10.56764/hpu2.jos.2023.2.3.59-66

Abstract

This paper deals with synchronization analysis problem for a class of fractional-order neural networks with unbounded delays. Using the Lyapunov function method combined with fractional Halanay inequality, we derive a novel sufficient condition for asymptotic stability of the error system resulting in two neural networks are synchronized. The obtained conditions are given in terms of linear matrix inequalities, which therefore can be efficiently checked. A numerical example is proposed to illustrate the effectiveness of the obtained results.

References

[1] J. Cao, H.X. Li, W. Daniel, “Synchronization criteria of Lur’e systems with time-delay feedback control”, Chaos, Solitons & Fractals, 23, pp.1285-1298, 2005, doi: 10.1016/S0960-0779(04)00380-7
[2] X.H. Chang, L. Zhang, J.H. Park, “Robust static output feedback H∞ control for uncertain fuzzy systems”, Fuzzy Sets. Syst., 273, pp.87-104, 2015, doi: 10.1016/j.fss.2014.10.023
[3] R. Coban, “A context layered locally recurrent neural network for dynamic system identification”, Engineering Applications of Artificial Intelligence, 26, pp.241-250, 2013, doi: 10.1016/j.engappai.2012.09.023
[4] K. Dietthelm, The analysis of fractional differential equations: An application oriented exposition using differential operators of Caputo type, Springer-Verlag, Berlin, 2010, doi: 10.1007/978-3-642-14574-2
[5] C. Ge, C.C. Hua, and X.P. Guan, “Master-slave synchronization criteria of Lur’e systems with time-delay feedback control”, Applied Mathematics and Computation, 244, pp.895-902, 2014, doi: 10.1016/j.amc.2014.07.045
[6] B.B. He, H.C. Zhou, “Asymptotic stability and synchronization of fractional order Hopfield neural networks with unbounded delay”, Math. Meth. Appl. Sci., 46(3), pp.3157-3175, 2021, doi: 10.1002/mma.8000
[7] B.B. He, H.C. Zhou, C.H. Kou and Y.Q. Chen, “New integral inequalities and asymptotic stability of fractional order systems with unbounded time delay”, Nonlinear Dynam., 94(2), pp.1523-1534, 2018, doi: 10.1007/s11071-018-4439-z
[8] D.T. Hong, N.H. Sau, M.V. Thuan, “New results on dissipativity analysis for a class of fractional-order static neural networks”, Circuits, Systems, and Signal Processing, 41, pp.2221-2243, 2022, doi: 10.1007/s00034-021-01888-2
[9] A. Kilbas, H. Srivastava, J. Trujillo, Theory and application of fractional differential equations, New York, Elsevier, 2006, doi: 10.3182/20060719-3-PT-4902.00008
[10] V. Lekshmikantham, S. Leela, J.V. Devi, Theory of fractional dynamical systems, Cambridge, 2009.
[11] Y. Li, Y.Q. Chen, I. Podlubny, “Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag--Leffler stability”, Computers & Mathematics with Applications, pp.59, doi: 10.1016/j.camwa.2009.08.019
[12] T. Li, S.M. Fei, Q. Zhu, and S. Cong, “Exponential synchronization of chaotic neural networks with mixed delays”, Neurocomputing, 71, pp.3005-3019, 2008, doi: 10.1016/j.neucom.2007.12.029
[13] S. Loghmanian, H. Jamaluddin, R. Ahmad, R. Yusof, M. Khalid, “Structure optimization of neural network for dynamic system modeling using multi-objective genetic algorithm”, Neural Computing and Applications, 21, pp.1281-1295, 2012, doi: 10.1007/s00521-011-0560-3
[14] N.H. Sau, M.V. Thuan, N.T.T. Huyen, “Passivity analysis of fractional-order neural networks with time-varying delay based on LMI approach”, Circuits, Systems, and Signal Processing, 39, pp.5906-5925, 2020, doi: 10.1007/s00034-020-01450-6
[15] H.T. Tuan, H. Trinh, “Stability of fractional-order nonlinear systems by Lyapunov direct method”, IET Control Theory Appl., 12, pp.2417-2422, 2018, doi: 10.1049/iet-cta.2018.5233
[16] H. Wang, Y.G. Yu, G.G. Wen, S. Zhang, “Stability analysis of fractional-order neural networks with time delay”, Neural Process Lett., 42, pp.479-500, 2015, doi: 10.1007/s11063-014-9368-3

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Published

29-12-2023

How to Cite

Duong, T.-H., & Vu-Thi, T.-L. (2023). Synchronization for fractional-order neural networks with unbounded delays. HPU2 Journal of Science: Natural Sciences and Technology, 2(3), 59–66. https://doi.org/10.56764/hpu2.jos.2023.2.3.59-66

Volume and Issue

Section

Natural Sciences and Technology