A method for the numerical computation of Hopf bifurcation

Abstract

This paper deals with the computation of Hopf bifurcations in parameter dependent ordinary differential equations. An algorithm based on an indirect method is presented. While the conventional method approaches the Hopf bifurcation point from the stationary solution, the proposed method detects the Hopf bifurcation points from the “dynamic” solution. A computation using the proposed algorithm is implemented for finding the Hopf bifurcation point of several cases, and the comparison with the results obtained by other methods is given. The proposed method is applicable for both autonomous and non-autonomous systems.