Detecting codimension two bifurcations with a pure imaginary pair and a simple zero eigenvalue. (English) Zbl 0760.65060
For two parameter dependent nonlinear dynamical systems \(\dot x =F(\lambda,\mu,x)\) the interest is in the numerical determination of a Hopf-steady state mode interaction. A straight forward extended system for this codimension two bifurcation is presented which is proved to have an isolated solution at the bifurcation point \((\lambda_ 0,\mu_ 0,x_ 0)\) of interest.
An efficient algorithm to solve the linear systems arising by Newton’s method is given. A numerical example for a tubular reactor is included.
An efficient algorithm to solve the linear systems arising by Newton’s method is given. A numerical example for a tubular reactor is included.
Reviewer: B.Werner (Hamburg)
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 65H17 | Numerical solution of nonlinear eigenvalue and eigenvector problems |
| 58E07 | Variational problems in abstract bifurcation theory in infinite-dimensional spaces |
