Transcritical and pitchfork bifurcation in differential algebraic equations without reduction

Abstract EN

In this paper, the system of differential algebraic equations (DAEs) are considered and sufficient conditions to make the origin undergoes a transcortical or a pitchfork bi¬furcation are given.

Those conditions talk about index one and index two DAE systems, and gotted by applying two strategies : depending on differential part and depending on constraint.

We generalize the work of [Stephen, 1990] and apply his strategy on index one and two DAEs.

His work applied on Ordinary differential equations (ODEs) with : 1.

equilibrium solution are dealt with instead of solution, and 2.

the shape of bifurcation diagram is looked for instead of looking for the stability of equilibrium solution.

Depending on this we can determine which kind of bifurcation will occur in the system of differential algebraic equations.

Investigate bifurcation points depending on only the constraint equation in [Ian, 1992] had considered here and upgraded to go with DAEs of index one and two.