Bogdanov–Takens bifurcation in a single inertial neuron model with delay

In this paper, we study a retarded functional differential equation modeling a single neuron with inertial term subject to time delay. Bogdanov–Takens bifurcation is investigated by using center manifold reduction and the normal form method for RFDE. We get the versal unfolding of the norm forms at the B–T singularity and show that the model can exhibit saddle-node bifurcation, pitchfork bifurcation, homoclinic bifurcation, heteroclinic bifurcation and double limit cycle bifurcation. Some numerical simulations are given to support the analytic results.