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HclinicBifurcationKit.jl

This Julia package aims at performing bifurcation analysis of Homoclinic / Heteroclinic orbits of Cauchy problems.

It builds upon BifurcationKit.jl (version ≥ 0.8) to perform continuation and numerical bifurcation analysis.

📦 Installation

Assuming that you already have Julia correctly installed, it suffices to install HclinicBifurcationKit in the standard way:

] add HclinicBifurcationKit

The package can also be installed directly from its repository:

] add https://github.com/bifurcationkit/HclinicBifurcationKit.jl

Capabilities

  • compute Homoclinic to Hyperbolic Saddle Orbits (HomHS) using orthogonal collocation or standard shooting
  • compute bifurcations of HomHS
  • start HomHS from a direct simulation
  • automatic branch switching to HomHS from a Bogdanov–Takens bifurcation point

📚 Citing this work

If you use this package for your work, we ask that you cite the following paper! Open source development strongly depends on this. It is referenced on HAL-Inria with the bibtex entry CITATION.bib.

🧑‍💻 Other software

There are several good softwares already available.

  • For continuation in small dimension, most software are listed on DSWeb. One can mention the widely used AUTO-07p and MATCONT. All these are very reliable and some address high co-dimension bifurcations.

  • For large scale problems, there is none.

In Julia, the present package seems to be the only one.