Symmetry and Bifurcation of Periodic

We consider a reaction-di#usion equation with Neumann boundary conditions and show that solutions to this problem may be obtained from a problem with periodic boundary conditions and equivariant under O(2) symmetry. We describe the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steadystate /Hopf and Hopf/Hopf. Neumann boundary conditions constrain the solutions to fixed-point spaces of the original symmetry group