Computation of D10-Equivariant Nonlinear Bifurcation Problems

New symmetric property, composed of equivariant condition, was generated near each bifurcation point in numerical simulation of Brusslator reaction diffusion model. It was found that when the equivariant condition is added to Brusselator model, numerical results can exhibit symmetry phenomena. Different bifurcation subgroups were verified to be the cause of the generation of this symmetry breaking property. This manifests the existence of equivariant nontrivial bifurcation solution in Brusselator model.Furthermore, it is shown that when bifurcation parameter is increased, different nontrivial bifurcation solution branches bifurcating from steady solution also appears correspondingly.