Research article

Global dynamic analysis of periodic solution for discrete-time inertial neural networks with delays

  • Received: 11 November 2020 Accepted: 11 January 2021 Published: 15 January 2021
  • MSC : 34C25, 34C13

  • This paper is devoted to studying global dynamic behaviours of periodic solutions of discrete-time inertial neural networks with delays by applying Mawhin's continuation theorem and some innovative mathematical analysis techniques. Finally, an numerical example is given to illustrate our theoretical results.

    Citation: Zejian Dai, Bo Du. Global dynamic analysis of periodic solution for discrete-time inertial neural networks with delays[J]. AIMS Mathematics, 2021, 6(4): 3242-3256. doi: 10.3934/math.2021194

    Related Papers:

  • This paper is devoted to studying global dynamic behaviours of periodic solutions of discrete-time inertial neural networks with delays by applying Mawhin's continuation theorem and some innovative mathematical analysis techniques. Finally, an numerical example is given to illustrate our theoretical results.


    加载中


    [1] D. Wheeler, W. Schieve, Stability and chaos in an inertial two-neuron system, Physica D, 105 (1997), 267–284.
    [2] J. Jian, L. Duan, Finite-time synchronization for fuzzy neutral-type inertial neural networks with time-varying coefficients and proportional delays, Fuzzy Set. Syst., 381 (2020), 51–67.
    [3] C. Long, G. Zhang, Z. Zeng, Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays, Neural Networks, 129 (2020), 193–202.
    [4] Y. Sheng, T. Huang, Z. Zeng, P. Li, Exponential Stabilization of Inertial Memristive Neural Networks With Multiple Time Delays, IEEE T. Cybernetics, 12 (2019), 1–10.
    [5] Z. Tu, J. Cao, T. Hayat, Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks, Neural Networks, 75 (2016), 47–55.
    [6] K. Babcock, R. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Physica D, 23 (1986), 464–469.
    [7] S. Hu, J. Wang, Global stability of a class of discrete-time recurrent neural networks, IEEE T. Circuits-I, 49 (2002), 1104–1117.
    [8] P. Wan, J. Jian, Global convergence analysis of impulsive inertial neural networks with time-varying delays, Neurocomputing, 245 (2017), 68–76.
    [9] Z. Tu, J. Cao, T. Hayat, Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays, Neurocomputing, 171 (2016), 524–531.
    [10] J. Wang, L. Tian, Global Lagrange stability for inertial neural networks with mixed time-varying delays, Neurocomputing, 235 (2017), 140–146.
    [11] C. Aouiti, E. A. Assali, I. B. Gharbia, Y. El Foutayeni, Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations, Neurocomputing, 357 (2019), 292–309.
    [12] C. Huang, H. Zhang, Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method, Int. J. Biomath., 12 (2019), 1950016.
    [13] K. Wang, Z. Teng, H. Jiang, Adaptive synchronization in an array of linearly coupled neural networks with reaction-diffusion terms and time delays, Commun. Nonlinear Sci., 17 (2012), 3866–3875.
    [14] F. Zheng, Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity, AIMS Mathematics, 6 (2021), 1209–1222.
    [15] J. Wang, H. Wu, Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling, IEEE T. Cybernetics, 44 (2017), 1350–1361.
    [16] B. Liu, L. Huang, Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with time-varying delays, Chaos, Solitons and Fractals, 32 (2007), 617–627.
    [17] H. Yin, B. Du, Stochastic patch structure Nicholsonis blowfies system with mixed delays, Adv. Differ. Equ., 2020 (2020), 1–11.
    [18] M. Xu, B. Du, Dynamic behaviors for reaction-diffusion neural networks with mixed delays, AIMS Mathematics, 5 (2020), 6841–6855.
    [19] H. Yin, B. Du, Q. Yang, F. Duan, Existence of homoclinic orbits for a singular differential equation involving p-Laplacian, J. Funct. Spaces, 2020 (2020), 1–7.
    [20] T. Zhou, Y. Liu, Y. Liu, Existence and global exponential stability of periodic solution for discrete-time BAM neural networks, Appl. Math. Comput., 182 (2006), 1341–1354.
    [21] L. Hien, L. Hai-An, Positive solutions and exponential stability of positive equilibrium of inertial neural networks with multiple time-varying delays, Neural Comput. Appl., 31 (2019), 6933–6943.
    [22] J. Yogambigai, M. Syed Ali, H. Alsulami, M. S. Alhodaly, Global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays, Chinese J. Phys., 65 (2020), 513–525.
    [23] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer, Berlin, 1977.
    [24] G. Zhang, Z. Zeng, J. Hu, New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays, Neural Networks, 97 (2018), 183–191.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2443) PDF downloads(162) Cited by(3)

Article outline

Figures and Tables

Figures(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog