Bifurcation Model for Nonlinear Equations

A bifurcation model for a nonlinear equation is introduced. Under the non-degeneracy condition (Definition 2.1), 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.