New version of PseudoArcLengthContinuation

Dear All,

I am writing this post to report a new version of my package PseudoArcLengthContinuation.jl. The focus of this new version is twofold, automatic branch switching at bifurcations (Branch point of Equilibrium and Periodic orbits, Hopf bifurcation) and the computation of periodic orbits (and their bifurcations). I have also greatly improved the interface thanks to some discussion with @tkf. I know rely on Setfield.jl to specify parameters.

More precisely, here are the most noticable changes

  • re-writing of most of the docs and tutorials
  • computation of stationary normal forms even if the kernel is not 1d, computation of the Hopf normal form
  • branch switching at branch points
  • branch switching at Hopf point for the 3 different methods to compute periodic orbits
  • branch switching at branch points of periodic orbits
  • threaded computation of multiple shooting
  • drastic improvement in the computation of the sparse Jacobian for computing periodic orbits based on finite differences. This is now done inplace, the speedup can be substantial.

I hope some of you will find it useful.

Please have a look at PseudoArcLengthContinuation.jl and at the docs. Feel free to suggest improvements, design choices and submit PR :slight_smile:

I would like to thank @tkf for being patient and answering my questions on discourse.



I make this quick announcement to inform that the (former) PseudoArcLengthContinuation has been renamed BifurcationKit.jl.

Sadly, I did not have the BOLS to call it BifurcationsOfLargeSystems.jl (that’s @antoine-levitt 's pun) .

More seriously, there is a which collect the most important changes in the package.