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Bifurcation in delay differential systems with triple-zero singularity. (Chinese. English summary) Zbl 1224.34239
Summary: The paper is devoted to the investigation of a triple-zero singularity and the generalized associated eigenspace. A reduced form for parameterized delay differential systems is obtained by using center manifold reduction and normal form calculation. The results given in the paper by {\it E. Freire, E. Gamero, A. J. Rodríguez-Luis} and {\it A. Algaba} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2799--2820 (2002; Zbl 1043.37042)] are employed to analyze the bifurcation behavior of the parameterized delay differential system with triple-zero singularity in detail and an example is presented to illustrate the results.

34K18Bifurcation theory of functional differential equations
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K19Invariant manifolds (functional-differential equations)