Bifurcations Associated with Three-Phase Polynomial Dynamical Systems and Complete Description of Symmetry Relations Using Discriminant Criterion
The behavior and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type-twisted fold is discover...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-12-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/16/1/14 |
| Summary: | The behavior and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type-twisted fold is discovered on the basis and within the frames of the elements of the developed DS qualitative theory. The discriminant criterion applied originally to two-phase quadratic polynomial DSs is extended to three-phase DSs investigated in terms of their coefficient matrices. Specific classes of D- and S-vectors are introduced and a complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion. |
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| ISSN: | 2073-8994 |