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Bifurcation in delay differential systems with triple-zero singularity. (Chinese) 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 E. Freire, E. Gamero, A. J. Rodríguez-Luis and 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.
MSC:
34K18Bifurcation theory of functional differential equations
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K19Invariant manifolds (functional-differential equations)