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Precise computation of Hopf bifurcation and two applications. (English) Zbl 1002.37041

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.

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
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