New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative numerical study (Q1059377)

The authors propose two new algorithms for the numerical evaluation of Hopf bifurcation points. In contrast to two earlier published techniques [cf. the second author, SIAM J. Appl. Math. 38, 103-107 (1980; Zbl 0462.65046); Chem. Engrg. Sci. 34, 1078-1080 (1979)] they do not require the computation of the coefficients of the characteristic polynomials. Numerical experiments are performed for two typical examples from chemical reaction engineering consisting of systems of four ordinary differential equations in order to compare the effectiveness of the four algorithms with respect to memory requirements, arithmetical operations and domain and rate of convergence.