A Homotopy Method Of Switching Solution Branches At The Pitchfork Bifurcation Point
Yu Hao Cong 1, Zheng You Zhu 21 College of Mathematical Sciences, Shanghai Teachers University, Shanghai 200234, China
2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China / Department of Mathematics, Shanghai University, Shanghai 200072, China
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 stardard continuation procedure is only used. Some numerical examples are given to illustrate the effectiveness of this method.
Key words: Homotopy method; Switching solution branches; Pitchfork point.