English

Transition from rotating waves to modulated rotating waves on the sphere

Dynamical Systems 2009-11-11 v1 Classical Analysis and ODEs

Abstract

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.

Keywords

Cite

@article{arxiv.math/0501492,
  title  = {Transition from rotating waves to modulated rotating waves on the sphere},
  author = {Adela N. Comanici},
  journal= {arXiv preprint arXiv:math/0501492},
  year   = {2009}
}