Stationary states of the Hartline-Ratliff model
type: Item
instance of: scholarly article
title: Stationary states of the Hartline-Ratliff model
zbMATH Open document ID: 0643.92009
DOI: 10.1007/BF00319520
author: B. George
published in: Biological Cybernetics
publication date: 1987-01-01T00:00:00Z
review text: The dynamics of the considered neural nets are given by \(\dot x+x=c- \gamma B \vartheta(x)\), where c is the input, B the inhibition matrix (not necessarily symmetric), \(\gamma=1\) and the nonlinearity \(\vartheta(x)=\max(x,0)\). The unique stationary state is locally asymptotically stable iff \(I+B\) has all principial submatrices (1) strictly positive, and (2) with eigenvalues in the right half-plane. (1) guarantees unique solutions for the time-independent case. If the spectral radius of B is less than 1, global asymptotical stability follows. The results are compared with other contributions (bifurcations for large \(\gamma\), competitive systems theory etc.) and interpreted in terms of the crab Limulus nervous system.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 37A30
zbMATH DE Number: 4049450
zbMATH Keywords: Hartline-Ratliff model
zbMATH Keywords: uniqueness of stationary states
zbMATH Keywords: neurodynamics
zbMATH Keywords: neural nets
zbMATH Keywords: global asymptotical stability
zbMATH Keywords: Limulus nervous system
reviewed by: J.Horejs
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00319520
OpenAlex ID: W2062901806
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description: scientific article; zbMATH DE number 4049450