Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Neurodynamics with spatial self-organizations

  • 29 Accesses

  • 6 Citations


A neural network architecture with self-organization in phase and actual space is proposed and discussed. Special type of differential local interconnections simulating diffusion, dispersion, and convection were investigated. It is shown that these interconnections are responsible for biological pattern formation in a homogeneous neural structure. The model suggests a phenomenological explanation of the mechanisms of edge detection in vision process.

This is a preview of subscription content, log in to check access.


  1. Amari S (1983) Field theory of self-organizing neural nets. IEEE Trans Syst Man Cybern 13:741–748

  2. Appel P (1953) Traite de mecanique rationelle, Part II Sect. XXV. Gauthier-Villars, Paris

  3. Hurlbert A, Poggio T (1989) Making machines (and art int). See Art. Int. Debate, pp 213–239

  4. Sakaguchi Y (1990) Topographic organization of nerve field with teacher signal. Neural Network 3:411–421

  5. Whitham G (1972) Linear and nonlinear waves. Wiley, New York, pp 19–25, 460–466

  6. Zak M (1989a) Terminal attractors in neural networks. Neural Networks 2:259–274

  7. Zak M (1989b) The least constraint principle for learning in neurodynamics. Phys Lett A 135:25–28

Download references

Author information

Correspondence to M. Zak.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zak, M. Neurodynamics with spatial self-organizations. Biol. Cybern. 65, 121–127 (1991).

Download citation


  • Neural Network
  • Convection
  • Edge Detection
  • Pattern Formation
  • Network Architecture