Tutorials

There are three levels of tutorials:

1. fully automatic bifurcation diagram (aBD) computation (only for equilibria): one uses the function bifurcationdiagram and let it compute the diagram fully automatically. Note that you may have to tune the options before hand. Another possibility is to use deflated continuation.
2. semi-automatic bifurcation diagram computation: one uses automatic branch switching (aBS) to compute branches at specified bifurcation points
3. manual bifurcation diagram computation: one does not uses automatic branch switching. This has only educational purposes and for complex problems where aBS fails.

Example(s) for ODE

• Neural mass equation (automatic)

Bifurcation of Equilibria

• Temperature model (simplest example for equilibria)
• Snaking in the 2d Swift-Hohenberg equation
• A generalized Bratu–Gelfand problem in two dimensions
• Temperature model with ApproxFun (intermediate)
• The Swift-Hohenberg equation (non-local) on the GPU (Advanced)

Automatic bifurcation diagram

• Swift-Hohenberg equation 1d (Automatic)
• Automatic diagram of 2d Bratu–Gelfand problem (Intermediate)
• Deflated Continuation in the Carrier Problem

Solving PDEs using Finite elements with Gridap.jl

• 2d Bratu–Gelfand problem with Gridap.jl (Intermediate)

Bifurcation diagrams with periodic orbits

• Brusselator 1d (automatic)
• Brusselator 1d (advanced user)
• Brusselator 1d with periodic BC (experienced user)
• Period doubling in the Barrio-Varea-Aragon-Maini model
• Complex Ginzburg-Landau 2d
• Complex Ginzburg-Landau 2d (shooting)
• Langmuir–Blodgett transfer model (really advanced)

Bifurcation diagrams with waves