Fast computation for saddle-node bifurcation points of general nonlinear system with decoupled parameters

A very fast method for computing the saddle-node bifurcation point of general nonlinear systems with decoupled parameters is developed in this paper. The speed of the developed method is achieved through two factors. One factor is a new set of characteristic equations for the saddle-node bifurcation point which is of dimension n+1, instead of 2n+1, which is traditionally required in n-dimensional decoupled parameter-dependent nonlinear equations. The other factor is a new effective scheme for estimating the location of a desired saddle-node bifurcation point and its associated bifurcation value. The estimated location and value provide a good initial guess for computing the desired saddle-node bifurcation points. The proposed solution method has been applied to a set of 416-dimensional decoupled parameter-dependent nonlinear equations to illustrate its effectiveness and accuracy