Bifurcation of periodic solutions of delay differential equation with two delays. (Q1406985)

The article extends Kaplan-Yorke's method for the existence of periodic solutions to scalar delay differential equations with two delays of the type \[ \dot x(t) = (\pm)F(x(t),x(t-r_1),x(t-r_2)), \] where \(F\) is odd and satisfies additional symmetry properties, and the delays \(r_1\) and \(r_2\) have a particular (rational) ratio. Furthermore, the authors study Hopf and saddle-node bifurcations of periodic solutions for the equation with parameters, and give conditions under which these bifurcations occur.