Neural Computation, Vol 9, 319-336, Copyright © 1997 by The MIT Press
Effect of Delay on the Boundary of the Basin of Attraction in a Self-Excited Single Graded-Response Neuron
K. Pakdaman, C. P. Malta, C. Grotta-Ragazzo and J.-F. Vibert
Little attention has been paid in the past to the effects of interunit
transmission delays (representing axonal and synaptic delays) on the
boundary of the basin of attraction of stable equilibrium points in neural
networks. As a first step toward a better understanding of the influence
of delay, we study the dynamics of a single graded-response neuron with a
delayed excitatory self-connection. The behavior of this system is
representative of that of a family of networks composed of graded-response
neurons in which most trajectories converge to stable equilibrium points
for any delay value. It is shown that changing the delay modifies the
'location' of the boundary of the basin of attraction of the stable
equilibrium points without affecting the stability of the equilibria. The
dynamics of trajectories on the boundary are also delay dependent and
influence the transient regime of trajectories within the adjacent basins.
Our results suggest that when dealing with networks with delay, it is
important to study not only the effect of the delay on the asymptotic
convergence of the system but also on the boundary of the basins of
attraction of the equilibria.
