More on ordinary differential equations which yield periodic solutions of delay differential equations (Q1323112)

A Poincaré operator for the system \({dx \over dt} = - \lambda x - F(x)\) is defined for finding its periodic solutions which have some symmetry property, where \(x = [x_ 1, x_ 2, x_ 3]^ T\), \(F(x) = [f(x_ 2), f(x_ 3), f(x_ 1)]^ T\), \(\lambda\) is a real parameter and \(f\) is an odd \(C^ 2\) function such that \(f'(0) = 1\), \(xf(x) > 0\) for \(x \neq 0\). Periodic solutions which arise in the vicinity of zero are also studied. Some global bifurcation results using the Browder ejective fixed point theorem are presented.