Du, Zhengdong; Hassard, Brian Precise computation of Hopf bifurcation and two applications. (English) Zbl 1002.37041 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 8, No. 4, 495-518 (2001). An algorithm is described for the computation of Hopf bifurcation coefficients for autonomous ordinary differential equations, by Lyapunov-Schmidt reduction. The defining equations are solved using interval arithmetic. Nondegeneracy conditions and genericity of the unfolding are checked. The algorithm is applied to examples from an enzyme-catalyzed reaction model and to the Hodgkin-Huxley nerve conduction model. Reviewer: Ale Jan Homburg (Amsterdam) MSC: 37M20 Computational methods for bifurcation problems in dynamical systems 65P30 Numerical bifurcation problems 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) 34C23 Bifurcation theory for ordinary differential equations 37Gxx Local and nonlocal bifurcation theory for dynamical systems 65G20 Algorithms with automatic result verification 65G40 General methods in interval analysis Keywords:algorithm; computation of Hopf bifurcation coefficients; autonomous ordinary differential equations; Lyapunov-Schmidt reduction; interval arithmetic; enzyme-catalyzed reaction; Hodgkin-Huxley nerve conduction PDFBibTeX XMLCite \textit{Z. Du} and \textit{B. Hassard}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 8, No. 4, 495--518 (2001; Zbl 1002.37041)