caa a22 4500 445362022 CHVBK 20180317142918.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11071-010-9914-0 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9914-0 Practical computation of normal forms oftheBogdanov-Takens bifurcation [Elektronische Daten] [Guojun Peng, Yaolin Jiang] In this paper, we study the Bogdanov-Takens (double-zero) bifurcations for any autonomous ODEs system, and derive simple computational formulae for both critical normal forms and generic norm forms. These formulae involve only coefficients of the Taylor expansions of its right-hand sides at the equilibrium. They are equally suitable for both numerical and symbolic evaluations and conveniently allow us to classify codimension2 Bogdanov-Takens bifurcations. Furthermore, we can use them to check whether there exist the original parameters such that a system presents the Bogdanov-Takens bifurcation, and compute the corresponding bifurcation curves with high precision. Two known models are used as test examples to demonstrate the advantages of this method. Springer Science+Business Media B.V., 2011 Normal form nationallicence Bogdanov-Takens bifurcation nationallicence Critical nationallicence Generic nationallicence Peng Guojun Department of Applied Mathematics, Xi'an Jiaotong University, 710049, Xi'an, P.R. China aut Jiang Yaolin Department of Applied Mathematics, Xi'an Jiaotong University, 710049, Xi'an, P.R. China aut Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 99-132 0924-090X 66:1-2<99 2011 66 11071 https://doi.org/10.1007/s11071-010-9914-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9914-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Peng Guojun Department of Applied Mathematics, Xi'an Jiaotong University, 710049, Xi'an, P.R. China aut NATIONALLICENCE 700 1- Jiang Yaolin Department of Applied Mathematics, Xi'an Jiaotong University, 710049, Xi'an, P.R. China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 99-132 0924-090X 66:1-2<99 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer