| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, Iss. 2, Apr, 2009, pp. 161-180 @2009 Society for Chaos Theory in Psychology & Life Sciences Effects of Delays on the Basin Boundary of Attraction in a Hopfield Network of Two Delay-Connecting Neurons Abstract: A continuous-time Hopfield neural network with two delay-connecting
neurons is considered in this paper. Some sufficient conditions for the
number and delay-independent stability of the equilibria in the network
are given analytically. It is necessary to classify the attraction domains
since multiple attractors coexist when the sufficient conditions are
satisfied. Thus, effects of the delays on the boundary separating the
basins of attraction of the stable equilibria are investigated analytically
and numerically. The results show that the evolution of the boundary depends
on the delays and is neither simple nor intuitive even if the delays do
not affect the stability of attractors. The results provide also the
possibility to design the network according to the memory pattern and storage. Keywords: delay differential equation, neural network, basin of attraction, stability, self-feedback control |