Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Bifurcations Associated with Three-Phase Polynomial Dynamical Systems and Complete Description of Symmetry Relations Using Discriminant Criterion

Version 1 : Received: 26 October 2023 / Approved: 26 October 2023 / Online: 26 October 2023 (11:23:12 CEST)

A peer-reviewed article of this Preprint also exists.

Shestopalov, Y.; Shakhverdiev, A.; Arefiev, S.V. Bifurcations Associated with Three-Phase Polynomial Dynamical Systems and Complete Description of Symmetry Relations Using Discriminant Criterion. Symmetry 2024, 16, 14. Shestopalov, Y.; Shakhverdiev, A.; Arefiev, S.V. Bifurcations Associated with Three-Phase Polynomial Dynamical Systems and Complete Description of Symmetry Relations Using Discriminant Criterion. Symmetry 2024, 16, 14.

Abstract

The behaviour 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 complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion.

Keywords

symmetry; equivalence relations; bifurcations; polynomial quadratic dynamical system; qualitative theory; singularities; discriminant criterion

Subject

Computer Science and Mathematics, Applied Mathematics

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