Stationary states of the Hartline-Ratliff model
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.
scientific article; zbMATH DE number 4049450
scientific article