Neural Processing Letters

, Volume 49, Issue 1, pp 331–345 | Cite as

Discrete Analogue for a Class of Impulsive Cohen–Grossberg Neural Networks with Asynchronous Time-Varying Delays

  • Liangliang Li
  • Chuandong LiEmail author


This paper presents the exponential stability preservation in simulations of an impulsive Cohen–Grossberg neural networks with asynchronous time delays. By semi-discrete technique and impulsive maps as discrete representations of the nonlinear impulsive networks, difference equations formulated is obtained. And developing a new delay impulsive discrete time differential inequality, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence in Lyapunov sense of the discussed discrete time delayed Cohen–Grossberg system. It is show that the discrete time technique can preserve the equilibrium point of the continuous time model. Finally, one numerical example with simulation shows the effectiveness of the obtained results.


Semi-discretisation Exponential convergence Impulsive discrete time difference equations 



The authors are grateful for the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant Nos. KJ1710253, KJ1601002), the Youth Fund of Chongqing Three Gorges University(Grant No. 16QN14), and the support of the National Natural Science Foundation of China (61633011, 11601047), Project supported by Key Laboratory of Chongqing Municipal Institutions of Higher Education (Grant No. [2017]3).


  1. 1.
    Cohen M, Grossberg S (1983) Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13:815–826MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Mohamad S, Gopalsamy K (2003) Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl Math Comput 135:17–38MathSciNetzbMATHGoogle Scholar
  3. 3.
    Li X, Liu B, Wu J (2016) Sufficient stability conditions of nonlinear differential systems under impulsive control with state-dependent delay. IEEE Trans Automat Control. Google Scholar
  4. 4.
    Rios J, Alanis A, Arana-Daniel N, Lopez-Franco C (2017) Recurrent high order neural observer for discrete-time non-linear systems with unknown time-delay. Neural Process Lett 46(2):663–679CrossRefGoogle Scholar
  5. 5.
    Wen S, Zeng Z, Huang T, Zeng Q (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26:1493–1502MathSciNetCrossRefGoogle Scholar
  6. 6.
    Huang T, Li C, Duan S, Starzyk J (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23:866–875CrossRefGoogle Scholar
  7. 7.
    He W, Chen G, Han Q, Qian F (2017) Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. Inf Sci 380(20):145–158CrossRefGoogle Scholar
  8. 8.
    Zhang X, Li C, Huang T (2017) Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses. Neural Netw 93:176–184CrossRefGoogle Scholar
  9. 9.
    He W, Qian F, Cao J (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Netw 85:1–9CrossRefGoogle Scholar
  10. 10.
    Bose A, Ioannou P (2003) Analysis of traffic flow with mixed manualand semiautomated vehicles. IEEE Trans Intell Transp Syst 4(4):173–188CrossRefGoogle Scholar
  11. 11.
    Liu X, Chen T (2016) Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans Neural Netw Learn Syst 27(3):593–606MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wu A, Liu L, Huang T, Zeng Z (2017) Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments. Neural Netw 85:118–127CrossRefGoogle Scholar
  13. 13.
    Chen Z, Zhao D, Fu X (2009) Discrete analogue of high-order periodic Cohen–Grossberg neural networks with delay. Appl Math Comput 214:210–217MathSciNetzbMATHGoogle Scholar
  14. 14.
    Huang Z, Mohamad S, Gao F (2014) Multi-almost periodicity in semi-discretizations of a general class of neural networks. Math Comput Simul 101:43–60MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tu Z, Ding N, Li L, Feng Y, Zou L, Zhang W (2017) Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term. Appl Math Comput 311(15):118–128MathSciNetzbMATHGoogle Scholar
  16. 16.
    Aouiti C, M’hamdi M, Cherif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46:487–506CrossRefGoogle Scholar
  17. 17.
    Song Q, Yang X, Li C, Huang T, Chen X (2017) Stability analysis of nonlinear fractional-order systems with variable-time impulses. J Frankl Inst 354(7):2959–2978MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Mohamad S, Gopalsamy K (2000) Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math Comput Simul 53:1–39MathSciNetCrossRefGoogle Scholar
  19. 19.
    Li X, Song S (2013) Impulsive control for existence, uniqueness andglobal stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24:868–877CrossRefGoogle Scholar
  20. 20.
    Sun G, Zhang Y (2014) Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay. Neurocomputing 131(1):323–330CrossRefGoogle Scholar
  21. 21.
    Yang W, Wang Y, Zeng Z, Zheng D (2015) Multistability of discrete-time delayed Cohen–Grossberg neural networks with second-order synaptic connectivity. Neurocomputing 164:252–261CrossRefGoogle Scholar
  22. 22.
    Li L, Jian J (2015) Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays. J Comput Appl Math 277(15):23–35MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Jian J, Wan P (2017) Lagrange \(\alpha \)-exponential stability and \(\alpha \)-exponential convergence for fractional-order complex-valued neural networks. Neural Netw 91:1–10CrossRefGoogle Scholar
  24. 24.
    Liz E, Ferreiro J (2002) A note on the global stability of generalized difference equations. Appl Math Lett 15(6):655–659MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Xu H, Chen Y, Teo K (2010) Global exponential stability of impulsive discrete-time neural networks with time-varying delays. Appl Math Comput 217:537–544MathSciNetzbMATHGoogle Scholar
  26. 26.
    Zhong S, Li C, Liao X (2010) Global stability of discrete-time Cohen–Grossberg neural networks with impulses. Neurocomputing 73:3132–3138CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information EngineeringSouthwest UniversityChongqingChina
  2. 2.School of Mathematics and StatisticsChongqing Three Gorges UniversityChongqingChina

Personalised recommendations