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Stability and existence of periodic solutions in inertial BAM neural networks with time delay

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Abstract

In this paper, the global exponential stability and existence of periodic solutions for inertial BAM neural networks are investigated. The system is transformed to first-order differential equation with chosen variable substitution. Then, some new sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov function, using Weierstrass criteria and boundedness of solutions. Finally, an example is given to illustrate the effectiveness of the results.

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References

  1. Kosko B (1987) Adaptive bi-directional associative memories. Appl Optim 26:4947–4960

    Article  Google Scholar 

  2. Kosko B (1988) Bi-directional associative memo-ries. IEEE Trans Syst Man Cybern 18:49–60

    Article  MathSciNet  Google Scholar 

  3. Kosko B (1992) Neural networks and fuzzy systems—a dynamical system approach machine intelligence. Prentice-Hall, Englewood Cliffs, pp 38–108

    Google Scholar 

  4. Zhao HY (2002) Global stability of bidirectional associative memory neural networks with dis- tributed delays. Phys Lett A 297:182–190

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang J, Yang Y (2001) Global stability analysis of bi-directional associative memory neural networks with time delays. Int J Circuit Theor Appl 299:185–196

    Article  Google Scholar 

  6. Cao J, Dong M (2003) Exponential stability of delayed bi-directional associative memory neural networks. Appl Math Comput 142:333–339

    Article  MathSciNet  MATH  Google Scholar 

  7. Cao J, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13(2):457–463

    Article  Google Scholar 

  8. Cao J, Xiao M (2007) Stability and Hopf bifurcation in a simplified BAM neural networks with two time delays. IEEE Trans Neural Netw 18(2):416–430

    Article  MathSciNet  Google Scholar 

  9. Song Q, Cao J (2005) Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms. Chaos Solitons Fractals 23:421–430

    Article  MathSciNet  MATH  Google Scholar 

  10. Song Q, Cao J (2007) Dynamics of bidirectional associative memory networks with delays and reaction-diffusion terms. Nonlinear Anal 8:345–361

    Article  MathSciNet  MATH  Google Scholar 

  11. Song Q, Cao J, Li YM (2005) Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms. Phys Lett A 335:231–225

    Article  Google Scholar 

  12. Badcock KL, Westervelt RM (1987) Dynamics of simple electronic neural networks. Phys D 28:305–316

    Article  MathSciNet  Google Scholar 

  13. Tani J (1992) Proposal of chaotic steepest descent method for neural networks and analysis of their dynamics. Electron Commun Jpn 75(4):62–70

    Article  MathSciNet  Google Scholar 

  14. Tani J, Fujita M (1992) Coupling of memory search and mental rotation by a nonequilibrium dynamics neural network. IEICE Trans Fundam Electron Commun Comput Sci E E75-A(5):578–585

    Google Scholar 

  15. Tani J (1996) Model-based learning for mobile robot navigation from the dynamical systems perspective. IEEE Trans Syst Man Cybern 26(3):421–436

    Article  Google Scholar 

  16. Li CG, Chen GR, Liao XF, Yu JB (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B 41:337–343

    Article  Google Scholar 

  17. Liu Q, Liao XF, Wang GY, Wu Y (2006) Research for Hopf bifurcation of an inertial two-neuron system with time delay. In: IEEE Proceeding GRC, pp 420–423

  18. Liu Q, Liao XF, Yang DG, Guo ST (2007) The research for Hopf bifurcation in a single inertial neuron model with external forcing. In: IEEE Proceeding GRC, pp 528–533

  19. Liu Q, Liao X, Liu Y, Zhou S, Guo S (2009) Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn 58:573–609

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu Q, Liao X, Guo S, Wu Y (2009) Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal Real World Appl 10:2384–2395

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work is supported by the Natural Science Foundation of Zhejiang Province (No.Y6100096) and the National Natural Science Foundation of China(No.10871226, No.10875078).

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing University, Shaoxing, 312000, People’s Republic of China

    Ke Yunquan & Miao Chunfang

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  1. Ke Yunquan
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  2. Miao Chunfang
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Correspondence to Ke Yunquan.

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Yunquan, K., Chunfang, M. Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput & Applic 23, 1089–1099 (2013). https://doi.org/10.1007/s00521-012-1037-8

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  • DOI: https://doi.org/10.1007/s00521-012-1037-8

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