Codimension two bifurcation in a simple delayed neuron model
This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model can exhibit pitchfork, Hopf, homoclinic bifurcation and saddle node bifurcation of periodic orbits. Some numerical simulations are given to support the analytic results.
codimension two bifurcation delayed neuron model homoclinic bifurcation saddle node bifurcation of periodic orbits