The papers by Farrell on deflated continuation are very good. I have not pushed my deflated continuation yet although it is sitting on my computer, it should be done this month.
I will also release a new version of the package soon with automatic branch switching, improved periodic orbit computations and a new interface for specifying problems… This should land at the same time you look at this hopefully.
For general continuation methods, it is huge field
- Govaerts, Numerical Methods for Bifurcations of Dynamical Equilibria .
- Mei, Numerical Bifurcation Analysis for Reaction-Diffusion Equations .
- Kuznetsov, Elements of Applied Bifurcation Theory .
- Waugh, Illingworth, and Juniper, “Matrix-Free Continuation of Limit Cycles for Bifurcation Analysis of Large Thermoacoustic Systems.”
- Dijkstra et al., “Numerical Bifurcation Methods and Their Application to Fluid Dynamics.”
- Keller, “The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity.”
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