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Dynamics of continuous-time bidirectional associative memory neural networks with impulses and their discrete counterparts

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  • Huo, Hai-Feng
  • Li, Wan-Tong

Abstract

This paper is concerned with the global stability characteristics of a system of equations modelling the dynamics of continuous-time bidirectional associative memory neural networks with impulses. Sufficient conditions which guarantee the existence of a unique equilibrium and its exponential stability of the networks are obtained. For the goal of computation, discrete-time analogues of the corresponding continuous-time bidirectional associative memory neural networks with impulses are also formulated and studied. Our results show that the above continuous-time and discrete-time systems with impulses preserve the dynamics of the networks without impulses when we make some modifications and impose some additional conditions on the systems, the convergence characteristics dynamics of the networks are preserved by both continuous-time and discrete-time systems with some restriction imposed on the impulse effect.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2218-2229
    DOI: 10.1016/j.chaos.2009.03.118
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    References listed on IDEAS

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    1. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    2. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    3. Chen, Jun & Cui, Baotong, 2008. "Impulsive effects on global asymptotic stability of delay BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1115-1125.
    4. Haydar Akça & Abdelkader Boucherif & Valéry Covachev, 2002. "Impulsive functional-differential equations with nonlocal conditions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    5. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    6. 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.
    7. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
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