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Tytuł artykułu

Discrete-time impulsive Hopfield neural networks with finite distributed delays

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
Neural Networks and Soft Computing/International Symposium (30.06-02.07.2005 ; Cracow, Poland)
Języki publikacji
EN
Abstrakty
EN
The discrete counterpart of a class of Hopfield neural networks with periodic impulses and finite distributed delays is introduced. A sufficient condition for the existence and global exponential stability of a unique periodic solution of the discrete system considered is obtained.
Rocznik
Strony
145--158
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
autor
autor
  • Department of Mathematical Science, Faculty of Science United Arab Emirates University, P. O. Box 17551, Al Ain, UAE
Bibliografia
  • [1] H. Akca, R. Alassar, V. Covachev, Z. Covacheva, E.A. Al-Zahrani. Continuous-time additive Hopfield-type neural networks with impulses. J. Math. Anal. AppL, 290: 436-451, 2004.
  • [2] H. Akca, R. Alassar, V. Covachev, Z. Covacheva. Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses. Dyn. Syst. AppL, 13: 75-90, 2004.
  • [3] V. Covachev, H. Akca, F. Yenicerioglu. Difference approximations for impulsive differential equations. Appl. Math. Comput, 121: 383-390, 2001.
  • [4] J. Freeman, D. Sakura. Neural Networks: Algorithms, Applications, and Programming Techniques. Addison-Wesley, Reading, Mass., 2001.
  • [5] K. Gopalsamy. Stability of artificial neural networks with impulses. Appl Math. Comput., 154: 783-813, 2004.
  • [6] K. Gopalsamy, X.Z. He. Stability in asymmetric Hopfield nets with transmission delays. Physica D, 76: 344-358, 1994.
  • [7] K. Gopalsamy, K.C. Issic, I.K.C. Leung, P. Liu. Global Hopf-bifurcation in a neural netlet. Appl. Math. Comput., 94: 171-192, 1998.
  • [8] D. Gulick. Encounters with Chaos. McGraw-Hill, New York, 1992.
  • [9] S. Haykin. Neural Networks, A Comprehensive Foundation. MacMillan, New York, 2000.
  • [10] R. Hecht-Nielsen. Neuro Computing. Addison-Wesley, Reading, Mass., 2000.
  • [11] J. Hertz, A. Krogh, R.G. Palmer. Introduction to the Theory of Neural Computation. Addison-Wesley Publishing Company, 1991.
  • [12] J.J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proc. National Acad. Sci., 79: 2554-2558, 1982.
  • [13] J.J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. National Acad. Sci., 81: 3088-3092, 1984.
  • [14] J.J. Hopfield, D.W. Tank. Computing with neural circuits; a model. Science, 233: 625-633, 1986.
  • [15] J. Jang, S. Lee, S. Shin, An optimization network for matrix inversion. In: D.Z. Anderson, ed., Neural Information Processing Systems, 397-401. American Institute of Physics, New York, 1988.
  • [16] Y. Li, L. Lu. Global exponential stability and existence of periodic solutions of Hopfield-type neural networks with impulses. Physics Letters A, 333: 62-71, 2004.
  • [17] Y. Li, W. Xing, L. Lu. Existence and global exponential stability of periodic solutions of a class of neural networks with impulses. Chaos, Solitons and Fractals, 27: 437-445, 2006.
  • [18] Y. Li, C. Yang. Global exponential stability on impulsive BAM neural networks with distributed delays. J. Math. Anal. Appi, 324: 1125-1139, 2006.
  • [19] C.M. Marcus, R.M. Westervelt. Stability of analog neural networks with delay. Phys. Rev. A, 39: 347-359, 1989.
  • [20| W. McCulloch, W. Pitts. A logical calculus of the ideas immanent in nervous activity. Buli. Math. Biophysics, 9: 127-147, 1943.
  • [21] G. Meinardus, G. Nurnberger, eds. Delay Equations, Approximation and Application. Birkhauser, Boston, 1985.
  • [22| S. Mohamad, K. Gopalsamy. Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math. Comput- Simul., 53: 1-39, 2000.
  • [23] S. Mohamad, K. Gopalsamy. Neuronal dynamics in time varying environments: Continuous and discrete time models. Discrete and Continuous Dynamical Systems, 6: 841-860.
  • [24] M. Morita. Associative memory with non-monotone dynamics. Neural Networks, 6: 115-126, 1993.
  • [25] D.W. Tank, J.J. Hopfield. Simple neural optimization networks: An A/D converter, signal decision circuit and a linear programming circuit. IEEE Trans. Circuit Syst., 33: 533-541, 1986.
  • [26] X. Yang, X. Liao, D.J. Evans, Y. Tang. Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Physics Letters A, 343: 108-116, 2005.
  • [27] X. Yang, X. Lisio, G.M. Megson, D.J. Evans. Global exponential periodicity of a class of neural networks with recent history distributed delays. Chaos, Solitons and Fractals, 25: 441-447, 2005.
  • [28] S. Yoshizawa, M. Morita, S. Amari. Capacity of associative memory using a nonmonotonic neuron model. Neural Networks, 6: 167-176, 1993.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0026-0011
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