Research article

Pseudo almost periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales

  • Received: 24 February 2021 Accepted: 05 July 2021 Published: 07 July 2021
  • MSC : 34K14, 34K20, 34N05, 92B20

  • This paper deals with a class of quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales. Based on the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for the considered networks. The results of this paper are completely new. Finally, an example is presented to illustrate the effectiveness of the obtained results.

    Citation: Xiaofang Meng, Yongkun Li. Pseudo almost periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales[J]. AIMS Mathematics, 2021, 6(9): 10070-10091. doi: 10.3934/math.2021585

    Related Papers:

  • This paper deals with a class of quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales. Based on the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for the considered networks. The results of this paper are completely new. Finally, an example is presented to illustrate the effectiveness of the obtained results.



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    [1] B. Xu, X. Liu, X. Liao, Global asymptonic stability of high-order Hopfield neural networks with time delays, Comput. Math. Appl., 45 (2003), 1729-1737. doi: 10.1016/S0898-1221(03)00151-2
    [2] X. Lou, B. Cui, Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, J. Math. Anal. Appl., 330 (2007), 144-158. doi: 10.1016/j.jmaa.2006.07.058
    [3] C. Ou, Anti-periodic solutions for high-order Hopfield neural networks, Comput. Math. Appl., 56 (2008), 1838-1844. doi: 10.1016/j.camwa.2008.04.029
    [4] Y. Yu, M. Cai, Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks, Math. Comput. Model., 47 (2008), 943-951. doi: 10.1016/j.mcm.2007.06.014
    [5] B. Xiao, H. Meng, Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks, Appl. Math. Model., 33 (2009), 532-542. doi: 10.1016/j.apm.2007.11.027
    [6] L. Duan, L. Huang, Z. Guo, Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations, Nonlinear Dynam., 77 (2014), 1469-1484. doi: 10.1007/s11071-014-1392-3
    [7] C. Xu, P. Li, Pseudo almost periodic solutions for high-order Hopfield neural networks with time-varying leakage delays, Neural Process. Lett., 46 (2017), 41-58. doi: 10.1007/s11063-016-9573-3
    [8] C. Xu, P. Li, Y. Pang, Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays, Math. Method. Appl. Sci., 39 (2016), 5720-5731. doi: 10.1002/mma.3957
    [9] F. Kong, Q. Zhu, K Wang, J. J. Nieto, Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator, J. Franklin. I., 356 (2019), 11605-11637. doi: 10.1016/j.jfranklin.2019.09.030
    [10] F. Kong, R. Rajan, Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time, Fuzzy Set. Syst., 411 (2021), 105-135. doi: 10.1016/j.fss.2020.07.009
    [11] W. Shen, X. Zhang, Y. Wang, Stability analysis of high order neural networks with proportional delays, Neurocomputing, 372 (2020), 33-39. doi: 10.1016/j.neucom.2019.09.019
    [12] Z. Dong, X. Zhang, X. Wang, State estimation for discrete-time high-order neural networks with time-varying delays, Neurocomputing, 411 (2020), 282-290. doi: 10.1016/j.neucom.2020.06.047
    [13] K. Gopalsamy, Kondalsamy, Leakage delays in BAM, J. Math. Anal. Appl., 325 (2007), 1117-1132. doi: 10.1016/j.jmaa.2006.02.039
    [14] P. Balasubramaniam, V. Vembarasan, R. Rakkiyappan, Leakage delays in T-S fuzzy cellular neural networks, Neural Process. Lett., 33 (2011), 111-136. doi: 10.1007/s11063-010-9168-3
    [15] R. Sakthivel, P. Vadivel, K. Mathiyalagan, A. Arunkumar, M. Sivachitra, Design of state estimator for bidirectional associative memory neural networks with leakage delays, Inform. Sciences, 296 (2015), 263-274. doi: 10.1016/j.ins.2014.10.063
    [16] C. Xu, L. Chen, P. Li, Effect of proportional delays and continuously distributed leakage delays on global exponential convergence of CNNs, Asian J. Control, 21 (2019), 2476-2483. doi: 10.1002/asjc.1942
    [17] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56. doi: 10.1007/BF03323153
    [18] Y. Li, C. Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., 2011 (2011), 341520.
    [19] Y. Li, L. Yang, Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales, Appl. Math. Comput., 242 (2014), 679-693.
    [20] W. Yang, W. Yu, J. Cao, F. Alsaadi, T. Hayat, Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales, Neurocomputing, 267 (2017), 241-260. doi: 10.1016/j.neucom.2017.05.089
    [21] Y. Li, X. Meng, L. Xiong, Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales, Int. J. Mach. Learn. Cyb., 8 (2017), 1915-1927. doi: 10.1007/s13042-016-0570-7
    [22] T. Isokawa, T. Kusakabe, N. Matsui, F. Peper, Quaternion neural network and its application, Berlin, Springer, 2003.
    [23] N. Matsui, T. Isokawa, H. Kusamichi, F. Peper, H. Nishimura, Quaternion neural network with geometrical operators, J. Intell. Fuzzy Syst., 15 (2004), 149-164.
    [24] M. Yoshida, Y. Kuroe, T. Mori, Models of hopfield-type quaternion neural networks and their energy functions, Int. J. Neural Syst., 15 (2005), 129-135. doi: 10.1142/S012906570500013X
    [25] Y. Li, J. Qin, B. Li, Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects, Math. Method. Appl. Sci., 42 (2019), 5-23. doi: 10.1002/mma.5318
    [26] N. Huo, B. Li, Y. Li, Existence and exponential stability of anti-periodic solutions for inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays, IEEE Access, 7 (2019), 60010-60019. doi: 10.1109/ACCESS.2019.2915935
    [27] Y. Li, H. Wang, X. Meng, Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays, IMA J. Math. Control I., 36 (2019), 983-1013. doi: 10.1093/imamci/dny015
    [28] Y. Li, J. Xiang, Existence and global exponential stability of almost periodic solution for quaternion-valued high-order Hopfield neural networks with delays via a direct method, Math. Method. Appl. Sci., 43 (2020), 6165-6180. doi: 10.1002/mma.6363
    [29] H. Wang, G. Wei, S. Wen, T, Huang, Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks, Appl. Math. Comput., 390 (2021), 125680.
    [30] C. Zhang, Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl., 151 (1994), 62-76.
    [31] T. Diagana, Pseudo almost periodic solutions to some differential equations, Nonlinear Anal. Theor., 60 (2005), 1277-1286. doi: 10.1016/j.na.2004.11.002
    [32] F. Kong, X. Fang, Pseudo almost periodic solutions of discrete-time neutral-type neural networks with delays, Appl. Intell., 48 (2018), 3332-3345. doi: 10.1007/s10489-018-1146-x
    [33] A. Zhang, Almost periodic solutions for SICNNs with neutral type proportional delays and D operators, Neural Process. Lett., 47 (2018), 57-70. doi: 10.1007/s11063-017-9631-5
    [34] A. Zhang, Pseudo almost periodic high-order cellular neural networks with complex deviating arguments, Int. J. Mach. Learn. Cyb., 10 (2019), 301-309. doi: 10.1007/s13042-017-0715-3
    [35] Y. Li, C. Wang, Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales, Adv. Differ. Equ., 2012 (2012), 77. doi: 10.1186/1687-1847-2012-77
    [36] A. Arbi, J. Cao, Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays, Neural Process. Lett., 46 (2017), 719-745. doi: 10.1007/s11063-017-9620-8
    [37] A. Zhang, Pseudo almost periodic solutions for neutral type SICNNs with D operator, J. Exp. Theor. Artif. In., 29 (2017), 795-807. doi: 10.1080/0952813X.2016.1259268
    [38] M. Bohner, A. Peterson, Dynamic equations on time scales: An introuduction with applications, Springer Science & Business Media, 2001.
    [39] M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Springer Science & Business Media, 2002.
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