TEKISLIKDA AYRIM DINAMIK SISTEMALAR LIMIT SIKLINI TAQRIBIY HISOBLASHNING XE USULI - Samsoqov Parviz Rustambek o’g’li (ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ, 2024)
In the theory of smooth dynamical systems, finding the periodic trajectory of a system is one of the important issues, and Gilbert's problem 16 is also precisely about evaluating the number of limit cycles from above in polynomial dynamical systems. This article explores the issue of calculating the limit cycle of certain quadratic dynamical systems at high resolution using the variation method of he. This problem corresponds to the intersection of algebraic geometry and the field of differential equations. The main purpose of the article is to study the variational method from a mathematical point of view and extend the field of application of this method by applying it to several dynamical systems.