Application of higher order bifurcation formulas

The conclusions of the Hopf bifurcation theorem are exact in an unspecified neighborhood of the critical value of the bifurcation parameter at which stability change takes place. It is shown that when the bifurcation parameter is far from its critical value and/or the system is highly nonlinear, it is necessary to use higher order bifurcation formulas to ensure good results. A brief description of the method and the applied algorithm is presented. Results that show the improvements obtained by the application of this approach to a chemical reactor are included