A Direct Method for the Computation of Hopf Bifurcation Points

Abstract

We present a method for the numerical computation of a Hopf bifurcation point of an evolution equation. An augmented time independent system of equations has to be solved, for which the Hopf bifurcation point is an isolated solution. In the case of a system of ordinary differential equations, we propose an efficient implementation of Newton’s method for the solution of the resulting system of algebraic equations. If the method is applied directly to a partial differential system with one space variable, a two point boundary value problem is obtained. We also compare this technique with a related method and results are given for two systems of partial differential equations, describing chemical reacting systems.