On Codimension 3 Singular Points of First-order Implicit Differential Equations

Authors

  • Yana Sergeevna Agakhanova Moscow Institute of Physics and Technology (State University), Dolgoprudniy, Russia
  • Aleksander Sergeevich Nikachev Moscow Institute of Physics and Technology (State University), Dolgoprudniy, Russia
  • Irina Nikolaevna Oblasova North-Caucasus Federal University, Stavropol, Russia

DOI:

https://doi.org/10.25728/assa.2023.23.01.1382

Keywords:

implicit differential equations, vector fields, singularities of mappings, fold, cusp, swallowtail

Abstract

We investigate local phase portraits of first-order implicit differential equations in a neighborhood of their singular points of codimension 3. Namely, we consider singular points where the lifted field of the equation on a surface is non-singular, but the projection of the surface to the phase plane has a singularity of one of three types: lips, beaks, swallowtail. We also consider generic bifurcations in one-parameter families of such equations.

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Published

2023-04-16

How to Cite

Agakhanova, Y. S., Nikachev, A. S., & Oblasova, I. N. (2023). On Codimension 3 Singular Points of First-order Implicit Differential Equations. Advances in Systems Science and Applications, 23(1), 8–21. https://doi.org/10.25728/assa.2023.23.01.1382

Issue

Vol. 23 No. 1 (2023): Advances in Systems Science and Applications

Section

Articles