Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model
Jacques Bélair, Sue Ann Campbell, P. van den Driessche
Source record
Source: Crossref
Published: Feb 1, 1996
DOI: 10.1137/s0036139994274526
Open original source ↗Source abstract
The effect of time delays on the linear stability of equilibria in an artificial neural network of Hopfield type is analyzed. The possibility of delay-induced oscillations occurring is characterized in terms of properties of the (not necessarily symmetric) connection matrix of the network.Such oscillations are possible exactly when the network is frustrated, equivalently when the signed digraph of the matrix does not require the Perron property. Nonlinear analysis (centre manifold computation) of a three-unit frustrated network is presented, giving the nature of the bifurcations taking place. A supercritical Hopf bifurcation is shown to occur, and a codimension-two bifurcation is unfolded.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.