arXiv math/05014922005-01-27math.DSmath.CA

Transition from rotating waves to modulated rotating waves on the sphere

Adela N. Comanici

DOI：: 10.1137/050631872

英文摘要：

We study non-resonant and resonant Hopf bifurcation of a rotating wave in SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced differential equations on so(3), the characterization of modulated rotating waves obtained by Hopf bifurcation of a rotating wave, as well as results regarding the resonant case. Our main tools are the equivariant center manifold reduction and the theory of Lie groups and Lie algebras, especially for the group SO(3) of all rigid rotations on a sphere.

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