Similar articles

Abstract: In this study, we investigate the problem of multiple mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained.

分数阶脉冲四元数神经网络多平衡点的Mittag-Leffler稳定性分析

[1]Abdurahman A, Jiang HJ, Teng ZD, 2015. Finite-time synchronization for memristor-based neural networks with time-varying delays. Neur Netw, 69:20-28.

[2]Cao JD, Xiao M, 2007. Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neur Netw, 18(2):416-430.

[3]Chen JJ, Zeng ZG, Jiang P, 2014. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neur Netw, 51:1-8.

[4]Chen XF, Song QK, Li ZS, et al., 2017. Stability analysis of continuous-time and discrete-time quaternion-valued neural networks with linear threshold neurons. IEEE Trans Neur Netw Learn Syst, 29(7):2769-2781.

[5]Hu J, Zeng CN, Tan J, 2017. Boundedness and periodicity for linear threshold discrete-time quaternion-valued neural network with time-delays. Neurocomputing, 267:417-425.

[6]Huang Y, Zhang H, Wang Z, 2012. Multistability and multiperiodicity of delayed bidirectional associative memory neural networks with discontinuous activation functions. Appl Math Comput, 219(3):899-910.

[7]Huang YJ, Li CH, 2019. Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function. Phys A, 527:121407.

[8]Khan H, Gómez-Aguilar J, Khan A, et al., 2019. Stability analysis for fractional order advection–reaction diffusion system. Phys A, 521:737-751.

[9]Kilbas AA, Srivastava HM, Trujillo JJ, 2006. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, the Netherlands.

[10]Li N, Zheng WX, 2020. Passivity analysis for quaternion-valued memristor-based neural networks with time-varying delay. IEEE Trans Neur Netw Learn Syst, 31(2):39-650.

[11]Li X, Ho DWC, Cao JD, 2019. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 99:361-368.

[12]Li XD, Ding YH, 2017. Razumikhin-type theorems for time-delay systems with persistent impulses. Syst Contr Lett, 107:22-27.

[13]Li XD, Wu JH, 2016. Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica, 64:63-69.

[14]Li XD, Zhang XL, Song SL, 2017. Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica, 76:378-382.

[15]Liu P, Zeng Z, Wang J, 2017. Multiple Mittag-Leffler stability of fractional-order recurrent neural networks. IEEE Trans Syst Man Cybern Syst, 47(8):2279-2288.

[16]Liu P, Zeng Z, Wang J, 2018. Multistability of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. IEEE Trans Neur Netw Learn Syst, 29(7):3000-3010.

[17]Liu Y, Zhang D, Lu J, 2017. Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays. Nonl Dynam, 87(1):553-565.

[18]Liu Y, Zhang D, Lou J, et al., 2018. Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neur Netw Learn Syst, 29(9):4201-4211.

[19]Nie XB, Liang JL, Cao JD, 2019. Multistability analysis of competitive neural networks with Gaussian-wavelet-type activation functions and unbounded time-varying delays. Appl Math Comput, 356:449-468.

[20]Pang DH, Jiang W, Liu S, et al., 2019. Stability analysis for a single degree of freedom fractional oscillator. Phys A, 523:498-506.

[21]Podlubny I, 1998. Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, San Diego, USA.

[22]Popa CA, Kaslik E, 2018. Multistability and multiperiodicity in impulsive hybrid quaternion-valued neural networks with mixed delays. Neur Netw, 99:1-18.

[23]Qi XN, Bao HB, Cao JD, 2019. Exponential input-to-state stability of quaternion-valued neural networks with time delay. Appl Math Comput, 358:382-393.

[24]Rakkiyappan R, Velmurugan G, Cao JD, 2014. Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonl Dynam, 78(4):2823-2836.

[25]Rakkiyappan R, Cao JD, Velmurugan G, 2015a. Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays. IEEE Trans Neur Netw Learn Syst, 26(1):84-97.

[26]Rakkiyappan R, Velmurugan G, Cao J, 2015b. Stability analysis of fractional-order complex-valued neural networks with time delays. Chaos Sol Fract, 78:297-316.

[27]Rakkiyappan R, Velmurugan G, Rihan FA, et al., 2016. Stability analysis of memristor-based complex-valued recurrent neural networks with time delays. Complexity, 21(4):14-39.

[28]Schauder J, 1930. Der fixpunktsatz in funktionalraümen. Stud Math, 2:171-180.

[29]Song QK, Chen XF, 2018. Multistability analysis of quaternion-valued neural networks with time delays. IEEE Trans Neur Netw Learn Syst, 29(1):5430-5440.

[30]Song QK, Yan H, Zhao ZJ, et al., 2016a. Global exponential linebreak newpage stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neur Netw, 79:108-116.

[31]Song QK, Yan H, Zhao ZJ, et al., 2016b. Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neur Netw, 81:1-10.

[32]Stamova I, 2014. Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonl Dynam, 77(4):1251-1260.

[33]Tyagi S, Abbas S, Hafayed M, 2016. Global Mittag-Leffler stability of complex valued fractional-order neural network with discrete and distributed delays. Rend Circol Matem PalermoSer 2, 65(3):485-505.

[34]Wang F, Yang YQ, Hu MF, 2015. Asymptotic stability of delayed fractional-order neural networks with impulsive effects. Neurocomputing, 154:239-244.

[35]Wang H, Yu Y, Wen G, et al., 2015. Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing, 154:15-23.

[36]Wang JJ, Jia YF, 2019. Analysis on bifurcation and stability of a generalized Gray-Scott chemical reaction model. Phys A, 528:121394.

[37]Wang LM, Song QK, Liu YR, et al., 2017. Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay. Neurocomputing, 243: 49-59.

[38]Wu AL, Zeng ZG, 2017. Global Mittag-Leffler stabilization of fractional-order memristive neural networks. IEEE Trans Neur Netw Learn Syst, 28(1):206-217.

[39]Yang XJ, Li CD, Song QK, et al., 2018. Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neur Netw, 105:88-103.

[40]Zeng ZG, Zheng WX, 2012. Multistability of neural networks with time-varying delays and concave-convex characteristics. IEEE Trans Neur Netw Learn Syst, 23(2):293-305.

[41]Zeng ZG, Huang TW, Zheng WX, 2010. Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans Neur Netw, 21(8):1371-1377.

[42]Zhang FH, Zeng ZG, 2018. Multistability and instability analysis of recurrent neural networks with time-varying delays. Neur Netw, 97:116-126.

[43]Zhang XX, Niu PF, Ma YP, et al., 2017. Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition. Neur Netw, 94:67-75.