Dynamics and control in an (n + 2)-neuron BAM network with multiple delays

The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present paper. By adopting the sum of the delays as the bifurcation parameter, we discuss the distribution of the roots of the characteristic equa- tion for high-dimension system in terms of stability switchestheoryandfurtherpresentsomesufficientcon- ditions for the occurrence of Hopf bifurcations. Analy- sis reveals that Hopf bifurcation will emerge after the given system loses its stability. Moreover, we derive explicit general formulae to determine the properties of bifurcation via the normal theory and the center manifold theorem. It is demonstrated that the sum of the delays can effectively affect the dynamics of the proposed system. Finally, an illustrative example is employedtoverifythevalidityofthetheoreticalresults obtained.