Piecewise Scaling in a Model of Neural Network Dynamics

  • German Chernykh
  • Yury Pis’mak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


Realistic neural network (RNN) model was proposed in 1981 by Kropotov and Pakhomov [4] for description of most important neuro-physiological dynamical mechanisms. In the modified RNN (MRNN) model [1,3] the defined by the Bogdanov-Hebb principle dynamics of interneuron interactions and a dissipation were introduced. In results the dynamics of the system appeared to be more stable and also a possibility arose to investigate the structure processes. The stable regimes of the MRNN model can be classified as periodical and non-periodical ones. A special case of non-periodical regime is the critical dynamics. It is characterized by consequences of quasi-periodical patterns of neuron activity with mean value of one equal 1/2. The distribution of durations of the patterns of such a kind is presented by a piecewise potential function.


Realistic neural network model critical dynamics piecewise potential distribution function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bogdanov, A.A.: Cognition from Historical Point of View. Saint-Petersburg (1901) (in Russian)Google Scholar
  2. 2.
    Chernykh, G.A., Pis’mak, Y.M.: Dynamics of Modified Kropotov-Pakhomov Neural Network Model. Neiroinformatika 2, 1–44 (2007) (in Russian)Google Scholar
  3. 3.
    Hebb, D.O.: The Organization of Behavior. A Neuropsychological Theory. Wiley & Sons, New York (1949)Google Scholar
  4. 4.
    Kropotov, Y.D., Pakhomov, S.V.: Mathematical Modeling of Mechanisms of Sygnal Processing by Neuron Populations in Brain. I. Statment of Problem and Main Features of Model. Fiziologiya Cheloveka 7, 152–162 (1981) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • German Chernykh
    • 1
  • Yury Pis’mak
    • 1
  1. 1.Department of Theoretical PhysicsState University Saint-PetersburgSaint-PetersburgRussia

Personalised recommendations