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Dynamics of a class of discrete-time neural networks and their continuous-time counterparts

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  • Mohamad, S.
  • Gopalsamy, K.

Abstract

The dynamical characteristics of continuous-time additive Hopfield-type neural networks are studied. Sufficient conditions are obtained for exponentially stable encoding of temporally uniform external stimuli. Discrete-time analogues of the corresponding continuous-time models are formulated and it is shown analytically that the dynamics of the networks are preserved by both continuous-time and discrete-time systems. Two major conclusions are drawn from this study: firstly, it demonstrates the suitability of the formulated discrete-time analogues as mathematical models for stable encoding of associative memories associated with external stimuli in discrete time, and secondly, it illustrates the suitability of our discrete-time analogues as numerical algorithms in simulating the continuous-time networks.

Suggested Citation

  • Mohamad, S. & Gopalsamy, K., 2000. "Dynamics of a class of discrete-time neural networks and their continuous-time counterparts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(1), pages 1-39.
    • Handle: RePEc:eee:matcom:v:53:y:2000:i:1:p:1-39
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    Cited by:

    1. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Chen, Shengshuang & Zhao, Weirui & Xu, Yong, 2009. "New criteria for globally exponential stability of delayed Cohen–Grossberg neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1527-1543.
    3. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    4. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    5. Yang, Xiaofan & Liao, Xiaofeng & Megson, Graham M. & Evans, David J., 2005. "Global exponential periodicity of a class of neural networks with recent-history distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 441-447.
    6. Jiang, Haijun & Teng, Zhidong, 2006. "Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 83-93.
    7. Zhang, Qiang & Xu, Xiaopeng Wei Jin, 2007. "Delay-dependent global stability results for delayed Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 662-668.
    8. Mohamad, Sannay, 2008. "Computer simulations of exponentially convergent networks with large impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 331-344.
    9. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    10. Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    11. Huo, Hai-Feng & Li, Wan-Tong, 2009. "Dynamics of continuous-time bidirectional associative memory neural networks with impulses and their discrete counterparts," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2218-2229.
    12. Huang, Zhenkun & Mohamad, Sannay & Gao, Feng, 2014. "Multi-almost periodicity in semi-discretizations of a general class of neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 43-60.

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