Normal forms for NFDEs with parameters and application to the lossless transmission line

A method for the computation of normal forms for neutral functional differential equations (NFDEs) with parameters is developed by considering an extension of phase space, based on the method of computing normal forms for FDEs with parameters previously introduced by Faria. The Hopf bifurcation of the differential difference equation is considered as an example of a circuit involving a lossless transmission line. The direction and stability of the bifurcating periodic solutions are also determined. Finally, numerical simulations are carried out to support the analytic results.