Classification of Parametric Constrained Bifurcation

If the constraint s boundary relates to the bifurcation parameter,a bifurcation is called parametric constrained one.Relying upon some substitution,parametric constrained bifurcation was trans formed to unconstrained bifurcation about new variables.Then general form of transition sets of the parametric constrained bifurcation was derived.The resultind icates thatonly constrained bifurcation set is influen ced by parametric constraints,other transition sets are the same as those of the nonparametric constrained bifurcation.Taking parametric constrained pitch fork bifurcation problems as examples,effects of param etric constraints on bifurcation classification were discussed further in detail.