Abstract
The finite-time synchronization (FTS) is investigated in this paper for delayed fractional-order quaternion-valued Cohen-Grossberg neural networks (FQVCGNNs). First, a fractional-order finite-time stability theorem is established by using the definition of fractional-order integral and reduction to absurdity. Next, two novel quaternion-valued feedback controller and quaternion-valued adaptive controller are designed respectively to achieve the FTS of FQVCGNNs. Then, without the participation of sign function, applying the non-decomposition method, the established finite-time stability theorem and constructing suitable quaternion-valued Lyapunov function, some less conservative and easily verifiable criteria are presented to ensure the FTS of the addressed system. Meanwhile, the settling time of FTS is effectively estimated, which depends on the controller parameters and the fractional order of the considered system. Finally, two numerical examples are provided to show the validity of the obtained results.
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References
Shanmugam L, Mani P, Rajan R, Joo YH (2020) Adaptive synchronization of reaction-diffusion neural networks and its application to secure communication. IEEE Trans Cybern 50(3):911–922
Wen S, Zeng Z, Huang T, Meng Q, Yao W (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502
Mislovaty R, Klein E, Kanter I, Kinzel W (2003) Public channel cryptography by synchronization of neural networks and chaotic maps. Phys Rev Lett 91:11–12
Chen T, Liu X, Lu W (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I Regul Pap 54(6):1317–1326
Wang L, Shen Y, Yin Q, Zhang G (2015) Adaptive synchronization of memristor-based neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 26(9):2033–2042
Wang N, Li X (2021) Optimal output synchronization control of a class of complex dynamical networks with partially unknown system dynamics. IEEE Trans Syst Man Cybern Syst 51(2):822–832
Hu C, Yu J, Jiang H, Teng Z (2011) Exponential synchronization of complex networks with finite distributed delays coupling. IEEE Trans Neural Netw 22(12):1999–2010
Gong S, Guo Z, Wen S, Huang T (2021) Finite-time and fixed-time synchronization of coupled memristive neural networks with time delay. IEEE Trans Cybern 51(6):2944–2955
Zhou F, Nie X (2022) A new Lyapunov function method to the fixed-time cluster synchronization of directed community networks. Neural Process Lett 54:2143–2164
Isokawa T, Kusakabe T, Matsui N, Peper F (2003) Quaternion neural network and its application. Lect Notes Artif Intell 2774:318–324
Liu Y, Zhang D, Lou J, Lu J, Cao J (2018) Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29(9):4201–4211
Liu Y, Zhang D, Lu J, Cao J (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inf Sci 360:273–288
Zhang D, Kou K, Liu Y, Cao J (2017) Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field. Neural Netw 94:55–66
Liu Y, Jiang B, Lu J, Cao J, Lu G (2020) Event-triggered sliding mode control for attitude stabilization of a rigid spacecraft. IEEE Trans Syst Man Cybern Syst 50(9):3290–3299
Jiang B, Liu Y, Kou K, Wang Z (2020) Controllability and observability of linear quaternion-valued systems. Acta Math Sin Engl Ser 36(11):1299–1314
Nie X, Liu P, Liang J, Cao J (2021) Exact coexistence and locally asymptotic stability of multiple equilibria for fractional-order delayed Hopfield neural networks with Gaussian activation function. Neural Netw 142:690–700
Zhang F, Zeng Z (2021) Multiple Mittag-Leffler stability of delayed fractional-order Cohen-Grossberg neural networks via mixed monotone operator pair. IEEE Trans Cybern 51(12):6333–6344
Du F, Lu J (2021) New criteria on finite-time stability of fractional-order Hopfield neural networks with time delays. IEEE Trans Neural Netw Learn Syst 32(9):3858–3866
Wu Z, Nie X, Cao B (2023) Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays. Neural Netw 160:132–147
Li H-L, Hu C, Zhang L, Jiang H, Cao J (2022) Complete and finite-time synchronization of fractional-order fuzzy neural networks via nonlinear feedback control. Fuzzy Sets Syst 443:50–69
Du F, Lu J, Zhang Q (2023) Delay-dependent finite-time synchronization criterion of fractional-order delayed complex networks. Commun Nonlinear Sci Numer Simul. https://doi.org/10.1016/j.cnsns.2022.107072
Hui M, Wei C, Zhang J, Iu H, Yao R, Bai L (2023) Finite-time synchronization of fractional-order memristive neural networks via feedback and periodically intermittent control. Commun Nonlinear Sci Numer Simul. https://doi.org/10.1016/j.cnsns.2022.106822
Zhang S, Liu X, Li X (2022) Finite-time synchronisation of delayed fractional-order coupled neural networks. Int J Syst Sci 53(12):2597–2611
Zhao F, Jian J (2022) Finite-time synchronization of fractional-order fuzzy Cohen-Grossberg neural networks with time delays. Iran J Fuzzy Syst 19(5):47–61
Xiao J, Zhong S (2019) Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties. Neurocomputing 363:321–338
Wu Z (2021) Multiple asymptotic stability of fractional-order quaternion-valued neural networks with time-varying delays. Neurocomputing 448:301–312
Yan H, Qiao Y, Duan L, Miao J (2021) Novel methods to global Mittag-Leffler stability of delayed fractional-order quaternion-valued neural networks. Neural Netw 142:500–508
Chen S, Li H-L, Bao H, Zhang L, Jiang H, Li Z (2022) Global Mittag-Leffler stability and synchronization of discrete-time fractional-order delayed quaternion-valued neural networks. Neurocomputing 511:290–298
Cohen M, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13(5):815–826
Qiao Y, Yan H, Duan L, Miao J (2020) Finite-time synchronization of fractional-order gene regulatory networks with time delay. Neural Netw 126:1–10
Liao H, Zhang Z (2023) Finite-time synchronization for coupled heterogeneous complex networks via differential inequality way. Neural Process Lett. https://doi.org/10.1007/s11063-023-11284-3
Ramajayam S, Rajavel S, Samidurai R, Cao Y (2023) Finite-time synchronization for T-S fuzzy complex-valued inertial delayed neural networks via decomposition approach. Neural Process Lett. https://doi.org/10.1007/s11063-022-11117-9
Hou T, Yu J, Hu C, Jiang H (2021) Finite-time synchronization of fractional-order complex-variable dynamic networks. IEEE Trans Syst Man Cybern Syst 51(7):4297–4307
Zhang Z, Cao J (2022) Finite-time synchronization for fuzzy inertial neural networks by maximum value approach. IEEE Trans Fuzzy Syst 30:1436–1446
Zhang W, Yang S, Li C, Li Z (2019) Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control. Neural Process Lett 50:2073–2086
Feng L, Yu J, Hu C, Yang C, Jiang H (2021) Nonseparation method-based finite/fixed-time synchronization of fully complex-valued discontinuous neural networks. IEEE Trans Cybern 51(6):3212–3223
Yang S, Yu J, Hu C, Jiang H (2021) Finite-time synchronization of memristive neural networks with fractional-order. IEEE Trans Syst Man Cybern 51(6):3739–3750
Yan H, Qiao Y, Duan L, Miao J (2022) New inequalities to finite-time synchronization analysis of delayed fractional-order quaternion-valued neural networks. Neural Comput Appl 34(12):9919–9930
Li H-L, Hu C, Zhang L, Jiang H, Cao J (2021) Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks. Appl Math Comput 409:126377
Wei W, Yu J, Wang L, Hu C, Jiang H (2022) Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control. Neural Netw 146:341–349
Wei R, Cao J, Abdel-Aty M (2021) Fixed-time synchronization of second-order MNNs in quaternion field. IEEE Trans Syst Man Cybern 51(6):3587–3598
Aouiti C, Bessifi M (2021) Periodically intermittent control for finite-time synchronization of delayed quaternion-valued neural networks. Neural Comput Appl 33(12):6527–6547
Deng H, Bao H (2019) Fixed-time synchronization of quaternion-valued neural networks. Phys A 527:121351
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
Du F, Lu J (2022) New results on finite-time stability of fractional-order Cohen-Grossberg neural networks with time delays. Asian J Control 24:2328–2337
Li H-L, Jiang H, Cao J (2020) Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays. Neurocomputing 385:211–219
Acknowledgements
This work was jointly supported by National Natural Science Foundation of China under Grant No. 61673111, the Fundamental Research Funds for the Central Universities under Grant 2242023K40010.
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Wu, Z., Nie, X. Finite-Time Synchronization of Fractional-Order Quaternion-Valued Delayed Cohen-Grossberg Neural Networks. Neural Process Lett 55, 12255–12271 (2023). https://doi.org/10.1007/s11063-023-11419-6
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DOI: https://doi.org/10.1007/s11063-023-11419-6