Phase trajectories of linear homogeneous autonomous dynamical systems of the third order

TL;DR

This paper explores the construction of phase trajectories near singular points in third-order linear homogeneous autonomous dynamical systems, offering expanded analysis and practical examples to deepen understanding.

Contribution

It provides a more comprehensive and grounded approach to analyzing phase trajectories near singular points in third-order systems, expanding on prior work.

Findings

Enhanced methods for constructing phase trajectories near singular points

Application of approach to multiple examples demonstrating effectiveness

Deeper theoretical understanding of third-order system behavior

Abstract

The proposed article is devoted to the study of the problem of constructing phase trajectories in the vicinity of a singular point. This paper presents a more expanded view of this problem in comparison with those previously considered by other authors and suggests a more meaningful and grounded development of this study. Numerous examples of the application of this approach to the study of trajectories at a singular point are given.