Abstract: We studied the stability, the existence of Hopf bifurcation and the stability bifurcation direction and bifurcation periodic solution  of the doubledelay flux neuron model by using  stability theory, central manifold theorem and other methods, and  some conclusions obtained by numerical simulation were given. The results show that the bifurcation periodic solution of the model is obtained within a certain time delay range, and  the increase of time delay can induce the spike discharge behavior.

Key words: Hindmarsh-Rose neuron, Hopf bifurcation, time delay, discharge behavior