Abstract
The behavior of center-indices, as introduced by J. Mallet-Paret & J. Yorke, is analyzed for two-parameter flows. The integer sum of center-indices along a one-dimensional curve in parameter space is called the H-index. A nonzero H-index implies global Hopf bifurcation. The index H is not a homotopy invariant. This fact is due to the occurrence of stationary points with an algebraically double eigenvalue zero, which we call B-points. To each B-point we assign an integer B-index, such that the H-index relates to the B-indices by a formula such as occurs in the calculus of residues.
This formula is easily applied to study global bifurcation of periodic solutions in diffusively coupled two-cells of chemical oscillators and to treat spatially heterogeneous time-periodic oscillations in porous catalysts.
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Communicated by M. Golubitsky
Dedicated to the memory of Charlie Conley
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Fiedler, B. Global Hopf bifurcation of two-parameter flows. Arch. Rational Mech. Anal. 94, 59–81 (1986). https://doi.org/10.1007/BF00278243
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DOI: https://doi.org/10.1007/BF00278243