Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, Iss. 2, April, 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

Jian Xu, Tongji University, Shanghai, P. R. China
Hui-lin Shang, Tongji University, Shanghai, P. R. China
Yu Huang, Tongji University, Shanghai, P. R. China

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