sentences:  The constant term in the Taylor series of the scaled bifurcation equation is called the algebraic bifurcation equation, and the implicit function theorem applied the bifurcation equations states that for each isolated solution of the algebraic bifurcation equation there is a branch of solutions of the original problem which passes through the singular point.Another type of singular point is a turning point bifurcation, or saddle-node bifurcation, where the direction of the parameter formula_2
  reverses as the curve is followed.The red curve in the figure above illustrates a turning point.