In this talk, we introduce the bifurcation model from the initial nonlinear term of a nonlinear equation. Under the non-degeneracy condition, our bifurcation model describes the bifurcation of solutions to the nonlinear equation. We also show how these models work for Dirichlet problem on the square. We observe a perturbation of rectangles to a square creates new bifurcation, which is not a limit of the bifurcations on rectangles.