Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions

doi:10.1088/1674-1056/ab7803

Abstract The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks (FDMNN) with parameters uncertainty and discontinuous activation functions. The relevant results are obtained under the framework of Filippov for such systems. Firstly, the novel feedback controller, which includes the discontinuous functions and time delays, is proposed to investigate such systems. Secondly, the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique. At the same time, the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated. In addition, by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems, the global asymptotic synchronization is achieved as a corollary. Finally, a numerical example is given to indicate the correctness of the obtained conclusions.

Keywords: fractional-order delayed memristive neural networks (FDMNN) parameters uncertainty discontinuous activation functions finite-time Mittag-Leffler synchronization

Received: 31 December 2019
Revised: 14 February 2020
Accepted manuscript online:

PACS:

02.30.Yy

(Control theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61703312 and 61703313).

Corresponding Authors: Zhixia Ding
E-mail: zxding89@163.com

Cite this article:

Chong Chen(陈冲), Zhixia Ding(丁芝侠), Sai Li(李赛), Liheng Wang(王利恒) Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions 2020 Chin. Phys. B 29 040202

[1]	Zhu S, Wang L D and Duan S K 2017 Neurocomputing 227 147
[2]	Hu X F, Feng G, Duan S K and Liu L 2016 IEEE Trans. Neural Netw. Learn. Syst. 28 1889
[3]	Li T S, Duan S K, Liu J and Wang L D 2018 Neural Computing and Applications 30 1939
[4]	Wen S P, Zeng Z G, Huang T W and Zhang Y D 2013 IEEE Trans. Fuzzy Syst. 22 1704
[5]	Wu A L and Zeng Z G 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 1919
[6]	Xiao J Y and Zhong S M 2018 Appl. Math. Comput. 323 145
[7]	Wu A L and Zeng Z G 2014 Neural Netw. 49 11
[8]	Yang X S, Cao J D and Liang J L 2016 IEEE Trans. Neural Netw. Learn. Syst. 28 1878
[9]	Ding Z X, Zeng Z G, Zhang H, Wang L M and Wang L H 2019 Neurocomputing 351 51
[10]	Ding Z X, Zeng Z G and Wang L M 2017 IEEE Trans. Neural Netw. Learn. Syst. 29 1477
[11]	Garza-Flores E and Alvarez-Borrego J 2018 J. Mod. Opt. 65 1634
[12]	Zhang Y D, Yang X J, Cattani C, Rao R V, Wang S H and Phillips P 2016 Entropy 18 77
[13]	Shen K M and Yu W 2018 IEEE Trans. Signal Process. 66 2631
[14]	Mashayekhi S, Miles P, Hussaini M Y and Oates W S 2018 J. Mech. Phys. Solids 111 134
[15]	Wu A L and Zeng Z G 2017 IEEE Trans. Neural Netw. Learn. Syst. 28 206
[16]	Wei H Z, Li R X, Chen C R and Tu Z W 2017 Neural Process. Lett. 45 379
[17]	Bao H B, Cao J D and Kurths J 2018 Nonlinear Dyn. 94 1215
[18]	Wan L G, Zhan X S, Gao H L, Yang Q S, Han T and Ye M J 2019 Int. J. Syst. Sci. 50 1
[19]	Chen L P, Huang T W, Machado J A, Lopes A M, Chai Y and Wu R C 2019 Neural Netw. 118 289
[20]	Chen L P, Wu R C, Cao J D and Liu J B 2015 Neural Netw. 71 37
[21]	Zhang W W, Cao J D, Wu R C, Chen D Y and Alsaadi F E 2018 Chaos, Solitons and Fractals 117 76
[22]	Zhao W and Wu H Q 2018 Adv. Difference. Equ. 2018 213
[23]	Chen C and Ding Z X 2019 Discrete Dyn. Nat. Soc. 2019 8743482
[24]	Chen L P, Wu R C, He Y G and Yin L S 2015 Appl. Math. Comput. 257 274
[25]	Forti M and Nistri P 2003 IEEE Trans. Circuits Syst. I-Regul. Pap. 50 1421
[26]	Zhang L Z 2019 Physica A 531 121756
[27]	Garcia-Ojalvo J and Roy R 2001 Phys. Rev. Lett. 86 5204
[28]	Wu G C, Deng Z G, Baleanu D and Zeng D Q 2019 An Interdisciplinary Journal of Nonlinear Science 29 083103
[29]	Li R and Chu T G 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 840
[30]	Chen L P, Cao J D and Wu R C, Tenreiro Machado J A, Lopes A M and Yang H J 2017 Neural Netw. 94 76
[31]	Ding Z X and Shen Y 2016 Neural Netw. 76 97
[32]	Chen C, Li L X, Peng H P, Yang Y X and Li T 2017 Neurocomputing 235 83
[33]	Chen J J, Zeng Z G and Jiang P 2014 Neural Netw. 51 1
[34]	Zhang W W, Cao J D, Alsaedi A and Alsaadi F E 2017 Math. Probl. Eng. 2017 1804383
[35]	Jia Y, Wu H Q and Cao J D 2019 Appl. Math. Comput. 30 124929
[36]	Peng X and Wu H Q 2018 Neural Comput. Appl. 2018
[37]	Zheng M W, Li L X, Peng H P, Xiao J H, Yang Y X, Zhang Y P and Zhao H. 2018 Commun. Nonlinear Sci. Numer. Simul. 59 272
[38]	Xiao J Y, Zhong S M, Li Y T and Xu F 2017 Neurocomputing 219 431
[39]	Li X F, Fang J, Zhang W B and Li H Y 2018 Neurocomputing 316 284
[40]	Zheng M W, Li L X, Peng H P, Xiao J H, Yang Y X and Zhao H 2017 Nonlinear Dyn. 89 2641
[41]	Velmurugan G, Rakkiyappan R and Cao J D 2016 Neural Netw. 73 36
[42]	Diethelm K 2010 Springer Science & Business Media (Berlin: Springer-Verlag) p. 49
[43]	Zhang S, Yu Y G and Wang H 2015 Nonlinear Anal.-Hybrid Syst. 16 104
[44]	Gu Y J, Yu Y G and Wang H 2016 Journal of the Franklin Institute 353 3657
[45]	Filippov A F 2013 Springer Science & Business Media (Netherlands: Springer) p. 48
[46]	Aubin J and Cellina A 2012 Springer Science & Business Media (Berlin: Springer-Verlag) p. 139
[47]	Li Y, Chen Y Q and Podlubny I 2009 Automatica 45 1965
[48]	Li Y, Chen Y Q and Podlubny I 2010 Comput. Math. Appl. 59 1810
[49]	Lam H and Leung F F 2006 Int. J. Bifur. Chaos 16 1435
[50]	Bao H B and Cao J D 2015 Neural Netw. 63 1
[51]	Peng X, Wu H Q and Cao J D 2019 IEEE Trans. Neural Netw. Learn. Syst. 30 2123
[52]	Peng X, Wu H Q, Song K and Shi J X 2017 Neural Netw. 94 46

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Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions

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