# gst: singular bifurcations, an approach

<< Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. >>

AA << then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked. >>️

Alexander Farutin, Chaouqi Misbah. Singular bifurcations and regularization theory. Phys. Rev. E 109, 064218. Jun 27, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064218

Alexander Farutin, Chaouqi Misbah. Singular Bifurcations : a Regularization Theory. arXiv: 2112.12094v2 [cond-mat.soft]. Jan 6, 2022. 

https://arxiv.org/abs/2112.12094 

Also: transition, singularity, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, singularity, bifurcation