Please use this identifier to cite or link to this item: https://repository.hneu.edu.ua/handle/123456789/37350
Title: Method for determining the cyclicity of singular points for quadratic systems of differential equations
Authors: Haluza O.
Akhiiezer O.
Malyarets L.
Voronin A.
Lebedev S.
Keywords: equilibrium state (singular point)
limit cycle
phase trajectory
Andronov-Hopf bifurcation
first three Lyapunov quantities
Issue Date: 2025
Citation: Haluza O. Method for determining the cyclicity of singular points for quadratic systems of differential equations / O. Haluza, O. Akhiiezer, L. Malyarets and other // Міжнародна конференція, присвячена 75-річчю з дня народження Володимира Маслюченка, 25-27 вересня 2025 р. : тези допов. - Чернівці, ЧНУ ім. Ю. Федьковича, 2025. - С. 125-129.
Abstract: In the theory of nonlinear dynamical systems described by differential equations with polynomial right-hand sides, the detection of hidden periodic modes (limit cycles) is still relevant. These periodic dynamic trajectories arise on the outskirts of the equilibrium point and determine the features of self-oscillating behavior that are characteristic only of purely nonlinear objects as a result of Andronov-Hopf bifurcations. The search for a rational method for determining the cyclicity of a singular point for a six-parameter system of differential equations with quadratic right-hand sides is relevant. This study is dedicated to solving this problem. Analysis of the mathematical model proposed in the work allowed us to calculate the first three Lyapunov quantities and, based on them, to formulate the conditions for the existence of limit cycles and propose a method for determining their multiplicity.
URI: https://repository.hneu.edu.ua/handle/123456789/37350
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