Multiple periodic orbits from Hopf bifurcation in a hierarchical neural network with D n x D n -symmetry and delays q

This paper concerns a model of hierarchical neural network with Dn x Dn-symmetry and time delays. The linear stability of the steady state is obtained via an artful factorization technique of the characteristic equation corresponding to the linearized system. And we also perform a delay-induced Hopf bifurcation analysis involving spatio-temporal patterns of bifurcated periodic solutions relying on the equivariant Hopf bifurcation theory for retarded functional differential equations and the representation method of Lie groups. Some numerical simulations for a simple example are carried out to demonstrate the appli-cation of our theoretical conclusion that multiple periodic orbits could occur simultaneously from Hopf bifurcation in the model. (c) 2020 Elsevier B.V. All rights reserved.