Bifurcation analysis in a simplified tri-neuron BAM network model with multiple delays

In this paper, we consider a three-dimensional delayed differential equation representing a bidirectional associate memory (BAM) neural network with three neurons and two discrete delays. By analyzing the number and stability of equilibria, the pitchfork bifurcation curve of the system is obtained. Furthermore, on the pitchfork bifurcation curve, by using the sum of two delays as the bifurcation parameter, we find that the system can undergo a Hopf bifurcation at the origin and the three-dimensional ordinary differential equation describing the flow on the center manifold is given.