Singularity structure of the Hopf bifurcation surface of a differential equation with two delays (Q1199840)

This work is concerned with the investigation of the structure of the Hopf bifurcation surface of the following differential equation with two delays: \[ {d\varphi(t) \over dt} =-\varphi(t)+\eta[f(\varphi(t-t_ 1))+f(\varphi(t-t_ 2))] \] where \(f(\varphi)=\cos(\varphi-\varphi_ 0)\), \(\varphi_ 0\) is a constant and \(t_ 1>t_ 2\) are positive parameters. When the real part of all the solutions of the characteristic equation are nonpositive, the corresponding bifurcation surface is called the first Hopf bifurcation surface. The authors use a geometric approach to analyze the characteristic equation, which enables them to obtain important results about the structure of the singularity of the first Hopf bifurcation surface.