A continuous-time network of K-winners-take-all (KWTA) neural circuit (NC) which is capable of identifying the largest K of N inputs, where a command signal 1 <= K < N is described. The network is described by a state equation with a discontinuous right-hand side and by an output equation. The state equation contains an impulse train defined by a sum of Dirac delta functions. Existence and uniqueness of the network work modes is analyzed. The main advantage of the network comparatively to other close analogs is widening convergence speed limitations to working modes. Theoretical results are derived and illustrated with computer simulation examples that demonstrate the network’s performance.

- E. Majani, R. Erlanson, and Y. Abu-Mostafa, “On the k-winners-take-all network,” in Advances in Neural Information Processing Systems 1, R. P. Lippmann, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann, 1989, pp. 634–642.
- J. Wang, “Analysis and design of a k-winners-takeall network with a single state variable and the Heaviside step activation function,” IEEE Trans. Neural Netw., vol. 21, no. 9, pp. 1496–1506, Sept. 2010.
- P. V. Tymoshchuk, “A simplified continuous-time model of analogue K-winners-take-all neural circuit”, in Proc. XI Int. Conf. “The Experience of Designing and Application of CAD Systems in Microelectronics”, Polyana-Svalyava, Ukraine, February 23–25, 2011, pp. 121–125.
- R. P. Lippmann, “An introduction to computing with neural nets,” IEEE Acoustics, Speech and Signal Processing Magazine, vol. 3, no. 4, pp. 4–22, Apr. 1987.
- P. Tymoshchuk and E. Kaszkurewicz, ”A winner-take all circuit using neural networks as building blocks,” Neurocomputing, vol. 64, pp. 375–396, Mar. 2005.
- P. Tymoshchuk, “Parallel rank-order filtering based on impulse Kwinners-take-all neural network,” Computer Systems and Networks, No 881, pp. 160–165, 2017.
- J. Lazzaro, S. Ryckebusch, M. A. Mahowald, and C. A. Mead, “Winner-take-all networks of O(N) complexity,” in Advances in Neural Information Processing Systems 1, R. P. Lippmann, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann, 1989, pp. 703–711.
- B. Sekerkiran and U. Cilingiroglu, “A CMOS K-winners-take-all circuits with 0(N) complexity,” IEEE Trans. Circuits Syst. II, vol. 46, no. 1, pp. 1–5, Jan. 1999.
- A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing. New York, NY, USA: Wiley, 1993.
- R. C. O’Reilly and Y. Munakata, Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain. Cambridge, MA: MIT Press, 2000.
- W. Maass, “Neural computation with winner-take-all as the only nonlinear operation,” in Advances in Information Processing Systems, vol.
- S. A. Solla, T. K. Leen, and K.-R. Mueller, Eds. Cambridge, MA: MIT Press, 2000, pp. 293–299.