Spatiotemporal Evolution of Large-Scale Bidirectional Associative Memory Neural Networks With Diffusion and Delays
Yunxiang Lu, Min Xiao, Jinling Liang, Jing Chen, Jinxing Lin, Zhengxin Wang, Jinde Cao
Abstract
In this article, the heterogeneity of the electromagnetic field is taken into account and thus the diffusion effect is introduced into the artificial neural network modeling. The first attempt of a class of large-scale bidirectional associative memory neural networks is provided, incorporating diffusion and delays. Using Coates’ flow diagram is able to efficiently and accurately capture the characteristic equations of large-scale reaction-diffusion neural networks. Furthermore, by tracing the distribution of characteristic roots driven by the time delay, a criterion on the local stability is determined and the critical tipping point caused by Hopf bifurcation is also predicted, respectively. Numerical simulations are eventually conducted to demonstrate the practical implications of the theory. It is shown that spatiotemporal dynamic behaviors of neural networks suggested are significantly affected by the transmission delay, the system scale, the self-feedback coefficient and the diffusivity.