Axioms, Год журнала: 2024, Номер 14(1), С. 8 - 8
Опубликована: Дек. 27, 2024
The work examines a seven-parameter, three-dimensional, autonomous, cubic nonlinear differential system. This system extends and generalizes the previously studied quadratic Hopf–Langford-type systems. First, by introducing polar coordinates in its phase space, we show that regarded can be reduced to two-dimensional Liénard system, which corresponds second-order equation. Then, present (in explicit form) polynomial first second integrals of systems considered type identifying those values their parameters for these exist. It is also proved generic equation factorizable if only corresponding admits integral special form. established each Hopf–Langford such integral, hence, respective factorizable.
Язык: Английский