Stability and bifurcation analysis of an annular delayed neural network with self-connection

A neural network model with three neurons and multiple delays is considered. Regarding the self-connection delay τsτs as the bifurcation parameter, linear stability and bifurcation including its direction and stability are investigated in this paper. By applying the normal form theory and the center manifold theorem, we obtain the direction of the Hopf-bifurcation and the stability of bifurcating periodic solutions. An example is given and numerical simulations are represented to illustrate the obtained results.