Numerical Computation of Coherent Structures in Spatially-Extended Systems

Authors

Daniele Avitabile

Abstract

This tutorial presents material and codes that I presented in a few talks on numerical bifurcation analysis. It aims to be a hands-on guide to perform numerical bifurcation analysis for PDEs or Integro-Differential Equations, starting from a given spatial discretisation. The material covers introductory concepts for the computation of branches of stationary states, and for stability computations. The accompanying codes give templates and workflows that have been adopted in several published papers. These notes, which are meant to be updated in the future, may be useful also for researchers who use other existing numerical bifurcation packages, and want to know more about how they work.

Links

BibTeX

@misc{avitabile2020,
  author = {Daniele Avitabile},
  title = {{Numerical Computation of Coherent Structures in Spatially-  Extended Systems}},
  month = may,
  year = 2020,
  publisher = {Zenodo},
  version = {v1.2-alpha},
  doi = {10.5281/zenodo.3821169},
  url = {https://doi.org/10.5281/zenodo.3821169}
}