On a Qualitative Picture of a Homogeneous Two-Dimensional System's Trajectory

Authors

  • Khusanov B. Associate Professor of the Department of Higher Mathematics, Samarkand State Institute of Architecture and Civil Engineering
  • Turaev M. Deputy Director for Science and Innovation, Candidate of Physical and Mathematical Sciences at Kattakurgan branch of Samarkand State University

Keywords:

global picture trajectory, isolated zero, classifications of integral manifolds, and - limit sets of trajectories, singular points, characteristic number, integral sector, parabolic sector, hyperbolic sector, elliptic sector, periodic trajectories, stable, unstable

Abstract

The article considers the global picture of the trajectories of a two-dimensional system

Here - is homogeneous continuous functions of degree of homogeneity having an isolated O at the beginning.

References

Н. П. Еругин. «Качественные исследования интегральных кривых системы дифференциальных уравнений». ПММ, Т. 14.в.6. 1950.

А. Пуанкаке. «О кривых, определяемых дифференциальными уравнениями». ГТТИ м.-л. 1947.

Ш. Р. Шарипов, Б. Хусанов. «Об обобщенных узлах и сёдлах в трехмерном пространстве». ДАН. УзССР, 1971, №11.

Khusanov B., Kulmirzayeva G. “Singular points classification of first order differential equations system not solved for derivatives”, International journal on integrated education, March 2021, Vol, 4 № 3 (2021)

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Published

2022-03-30

How to Cite

B., K. ., & M., T. . (2022). On a Qualitative Picture of a Homogeneous Two-Dimensional System’s Trajectory . European Multidisciplinary Journal of Modern Science, 4, 774–782. Retrieved from https://emjms.academicjournal.io/index.php/emjms/article/view/181

Issue

Vol. 4 (2022): March 2022

Section

Articles