Abstract
In this paper, we concern about the local stability and Hopf bifurcation on a class of high-dimensional ring-hub-structured neural networks. Firstly, the associated characteristic equation of system is obtained by the Coates formula. Then, by taking the time delay as the bifurcation parameter, the sufficient conditions ensuring the local stability and the occurrence of Hopf bifurcation of system are derived. Finally, the theoretical results are validated by the numerical simulations. It is found that the time delay can heavily affect the dynamics of proposed system. In addition, the onset of Hopf bifurcation is closely related to the number of neurons.
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