Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity |
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Authors: | Yingxiang Xu Mingyou Huang |
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Affiliation: | a School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China b School of Mathematics, Jilin University, Changchun 130012, China |
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Abstract: | The paper carries the results on Takens-Bogdanov bifurcation obtained in [T. Faria, L.T. Magalhães, Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity, J. Differential Equations 122 (1995) 201-224] for scalar delay differential equations over to the case of delay differential systems with parameters. Firstly, we give feasible algorithms for the determination of Takens-Bogdanov singularity and the generalized eigenspace associated with zero eigenvalue in Rn. Next, through center manifold reduction and normal form calculation, a concrete reduced form for the parameterized delay differential systems is obtained. Finally, we describe the bifurcation behavior of the parameterized delay differential systems with T-B singularity in detail and present an example to illustrate the results. |
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Keywords: | 34C37 34K17 34K18 37G05 37G10 |
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