Time Evaluation for WTA Hopfield Type Circuits Affected by Cross-Coupling Capacitances

  • Ruxandra L. Costea
  • Corneliu A. Marinov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5507)


A continuous time neural network of Hopfield type is considered. It is a W(inner) T(akes) A(ll) selector. Its inputs are capacitively coupled to model the parasitics or faults of overcrowded chip layers. A certain parameter setting allows the correct selection of the maximum element from an input list. As processing time is a performance criterion, we infer upper bounds of it, explicitly depending on circuit and list parameters. Our method consists of converting the system of nonlinear differential equations describing the circuit to a system of decoupled linear inequalities. The results are checked by numerical simulation.


Exponential Stability Maximal Element Global Exponential Stability Input List List Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two state neurons. Proc. Nat. Academy Sci. 81, 3088–3092 (1984)CrossRefGoogle Scholar
  2. 2.
    Hopfield, J.J., Tank, D.W.: Neural computation of decisions optimization problems. Biol. Cybern. 52, 141–152 (1985)MATHGoogle Scholar
  3. 3.
    Atkins, M.: Sorting by Hopfield nets. In: Proc. Int. Joint Conf. Neural Networks, Washington DC, vol. 2, pp. 65–68 (1992)Google Scholar
  4. 4.
    Dranger, T.S., Priemer, R.: Collective process circuit that sorts. IEE Proceedings-Circuits, Devices, Syst. 144, 145–148 (1997)CrossRefGoogle Scholar
  5. 5.
    Cao, J.: Global exponential stability of Hopfield neural networks. Int. J. Syst. Sci. 32(2), 233–236 (2001)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Majani, E., Erlanson, R., Abu-Mostafa, Y.: On the K-winner-take-all network. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems, vol. 1, pp. 634–642. Morgan-Kafmann, San Mateo (1989)Google Scholar
  7. 7.
    Zhang, Y., Heng, P.A., Fu, W.C.: Estimate of exponential convergence rate and exponential stability for neural network. IEEE Trans. Neural Networks 10(6), 1487–1493 (1999)CrossRefGoogle Scholar
  8. 8.
    Chen, T., Lu, W., Amari, S.: Global Convergence Rate of Recurrently Connected Neural Networks. Neural Computation 14, 2947–2957 (2002)CrossRefMATHGoogle Scholar
  9. 9.
    Calvert, B., Marinov, C.A.: Another K-winners-take-all analog neural network. IEEE Trans. Neural Networks 11, 829–838 (2000)CrossRefGoogle Scholar
  10. 10.
    Marinov, C.A., Calvert, B.D.: Performance analysis for a K-Winners-Take-All analog neural network: Basic theory. IEEE Trans. Neural Networks 14, 766–780 (2003)CrossRefGoogle Scholar
  11. 11.
    Cho, K.: Delay calculation capturing crosstalk effects due to coupling capacitors. Electronic Letters 41(8), 458–460 (2005)CrossRefGoogle Scholar
  12. 12.
    Marinov, C.A., Hopfield, J.J.: Stable computational dynamics for a class of circuits with O(N) interconnections capable of KWTA and rank extractions. IEEE Trans. Circuits and Systems, Part 1 52, 949–959 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Costea, R.L.: Artificial neural systems - Switching times for WTA circuits of Hopfield type. Doctoral Disertation, Polytechnic University of Bucharest (September 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ruxandra L. Costea
    • 1
  • Corneliu A. Marinov
    • 1
  1. 1.Department of Electrical EngineeringPolytechnic University of BucharestRomania

Personalised recommendations