A Homotopy Method of Switching Solution Branches at the Pitchfork Bifurcation Point (Journal of Computational Mathematics, 2001)
By introducing proper parameters in the original nonlinear systems, a continuation method for switching solution branches at a pitchfork point is proposed and their theories have been established in this paper. It is sufficient to implement this method that a standard continuation procedure is only used. Some numerical examples are given to illustrate the effectiveness of this method.
Keywords: Homotopy method; Switching solution branches; Pitchfork point.