HOPF BIFURCATION OF A FRACTIONAL-ORDER OCTONION-VALUED NEURAL NETWORKS WITH TIME DELAYS

摘要

In this paper,the hopf bifurcation of a fractional-order octonion-valued neural networks with time delays is investigated.With this constructed model all the parameters would belong to the normed division algebra of octonians.Because of the non-commutativity of the octonians,the fractional-order octonian-valued neural networks can be decomposed into four-dimensional realvalued neural networks.Furthermore,the conditions for the occurrence of Hopf bifurcation for the considered model are firstly given by taking time delay as a bifurcation parameter.Also we investigate their bifurcation when the system loses its stability.Finally,we give one numerical simulation to verify the effectiveness of the our proposed method.