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The Effect of Inhibitory Neurons on a Class of Neural Networks

In: Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment

Author

Listed:
  • Márton Neogrády-Kiss

    (Eötvös Loránd University Budapest, Institute of Mathematics
    Hungarian Academy of Sciences, Numerical Analysis and Large Networks Research Group)

  • Péter L. Simon

    (Eötvös Loránd University Budapest, Institute of Mathematics
    Hungarian Academy of Sciences, Numerical Analysis and Large Networks Research Group)

Abstract

The understanding of the effect of inhibitory neurons on neural networks’ dynamics is crucial to gain more insight into the biological process. Here we examine the dynamics of a special excitatory-inhibitory neural network where the network is complete. In this special case the dynamics has an order preserving property if the activation function is a positive bounded monotone increasing function. With a special choice of activation functions such as step functions we are able to analyse the whole dynamics. We do this in the case of two- and three-valued step functions. The three-valued case can exhibit stable limit cycles, so it would be worthwhile to analyse the dynamics on more complicated networks.

Suggested Citation

  • Márton Neogrády-Kiss & Péter L. Simon, 2020. "The Effect of Inhibitory Neurons on a Class of Neural Networks," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment, pages 97-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46306-9_7
    DOI: 10.1007/978-3-030-46306-9_7
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