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Normal forms for NFDEs with parameters and application to the lossless transmission line. (English) Zbl 1187.34094
Summary: A method for the computation of normal forms for neutral functional differential equations (NFDEs) with parameters is developed by considering an extension of the 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.
MSC:
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K40Neutral functional-differential equations
34K18Bifurcation theory of functional differential equations
34K60Qualitative investigation and simulation of models
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