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Bifurcation Points and Folds.

It is recommended that the detection of folds and bifurcation points be initially disabled. For example, if an equation has a ``vertical'' solution family then AUTO may try to locate one fold after another.

Generally, degenerate bifurcations cannot be detected. Furthermore, bifurcations that are close to each other may not be noticed when the pseudo-arclength step size is not sufficiently small. Hopf bifurcation points may go unnoticed if no clear crossing of the imaginary axis takes place. This may happen when there are other real or complex eigenvalues near the imaginary axis and when the pseudo-arclength step is large compared to the rate of change of the critical eigenvalue pair. A typical case is a Hopf bifurcation close to a fold. Similarly, Hopf bifurcations may go undetected if switching from real to complex conjugate, followed by crossing of the imaginary axis, occurs rapidly with respect to the pseudo-arclength step size. Secondary periodic bifurcations may not be detected for similar reasons. In case of doubt, carefully inspect the contents of the diagnostics file fort.9.


next up previous contents
Next: Floquet Multipliers. Up: Notes on Using AUTO. Previous: Correctness of Results.   Contents
Gabriel Lord 2007-11-19