Two-Parameters Bifurcation in Quasilinear Dierential-Algebraic Equations

In this paper, bifurcation of solution of guasilinear dierential-algebraic equations (DAEs) is studied. Whereas basic principle that quasilinear DAE is eventually reducible to an ordinary dierential equation (ODEs) and that this reduction so we can apply the classical bifurcation theory of the (ODEs). The taylor expansion applied to the reduced DAEs to prove that is equivalent to an ODE which is a normal form under some non-degeneracy conditions theorems given in this work deal with the saddle node,transcritical and pitchfork bifurcation with two-parameters. Some illustrated examples are given to explain the idea of the paper.