DOI: 10.3390/sym16010014 ISSN: 2073-8994

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

Yury Shestopalov, Azizaga Shakhverdiev, Sergey V. Arefiev
  • Physics and Astronomy (miscellaneous)
  • General Mathematics
  • Chemistry (miscellaneous)
  • Computer Science (miscellaneous)

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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