Two Notes on Continuous-Time Neurodynamical Systems

  • Ivan Daňo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


The neurodynamical model of recurrent networks in this paper is approached from an engineering perspective, i.e., to make networks efficient in terms of topology and capture dynamics of time-varying systems. Neural dynamics in that case can be considered from two aspects, convergence of state variables (memory recall) and the number, position, local stability and domains of attraction of equilibrium states (memory capacity). The purpose of this work is to investigate some relationship between Lyapunov exponents and the recurrent neural network model described by the concrete system of delay-differential equations.


Lyapunov exponents Recurrent networks Neurodynamical models Delay-differential equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Catsigeras, E.: Chaos and Stability in a Model of Inhibitory Neuronal Network. International Journal of Bifurcation and Chaos 20, 349–360 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Daňo, I., Haščák, A.: Neurodynamic systems. Elfa, Košice (2006) (in Slovak)Google Scholar
  3. 3.
    Demidovich, B.P.: Lectures on the Mathematical Theory of Stability. Nauka, Moscow (1967)zbMATHGoogle Scholar
  4. 4.
    Ďuračková, D.: From a biological neuron to an integrated circuit. Interlingua, Bratislava (2004) (in Slovak)Google Scholar
  5. 5.
    Huang, W., Huang, Y.: Chaos, Bifurcation and Robustness of a Class of Hopfield Neural Networks. International Journal of Bifurcation and Chaos 21, 885–895 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Marušiak, P., Olah, R.: Functional differential equations. Edis, Žilina (2000) (in Slovak) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ivan Daňo
    • 1
  1. 1.Department of Mathematics and Theoretical Informatics FEIThe Technical University of KošiceSlovakia

Personalised recommendations