Abstract

This chapter presents a new iterative method based on the existence conditions of Hopf bifurcation. By means of proposed method, the problem on how to deter- mine Hopf bifurcation point in an autonomous nonlinear system with bifurcation parameters is converted to how to solve a set of nonlinear algebraic equations. This method can determine both Hopf bifurcation point and the pure imaginary eigen-value pair of Jacobian matrix of a system at the same time. Thus, it can avoid some weakness in some existing methods, such as repeatedly solving the eigen-value whenever the chosen parameters are changed.

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