NUMERICAL ALGORITHM FOR DETERMINING HOPF BIFURCATION POINT OF NONLINEAR SYSTEM
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 determine 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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