Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays

A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a param eter space consisting of the sum of the time delays between the elements an d the product of the strengths of the connections between the elements. It is shown that the trivial fixed point may lose stability via a pitchfork bi furcation, a Hopf bifurcation, or one of three types of codimension-two bif urcations. Multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations.