Reversibility in polynomial systems of ODE's

DOI10.1016/j.amc.2018.05.051zbMath1427.34026OpenAlexW2810428220MaRDI QIDQ2335732

Tatjana Petek, Valery G. Romanovski, Mao'an Han

Publication date: 15 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.05.051

zbMATH Keywords

integrabilitysymmetriespolynomial systems of ODEstime-reversible system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (9)

The center problem and time-reversibility with respect to a quadratic involution for a class of polynomial differential systems with order 2 or 3 ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ SIXTEEN LARGE-AMPLITUDE LIMIT CYCLES IN A SEPTIC SYSTEM ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ Characterizing orbital-reversibility through normal forms ⋮ Integrability and multiple limit cycles in a predator-prey system with fear effect ⋮ Partial qualitative analysis of planar 𝓐Q-Riccati equations ⋮ Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point

Uses Software

• SINGULAR
• primdec

Cites Work

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• First integrals of local analytic differential systems
• The bifurcation of limit cycles in \(Z_n\)-equivariant vector fields
• The reversibility and the center problem
• Generalized involutive symmetry and its application in integrability of differential systems
• Time-reversal symmetry in dynamical systems: a survey
• Gröbner bases and primary decomposition of polynomial ideals
• The Sibirsky component of the center variety of polynomial differential systems.
• Bifurcation of limit cycles in 3rd-order \(Z_2\) Hamiltonian planar vector fields with 3rd-order perturbations
• A cubic system with twelve small amplitude limit cycles
• The Center and Cyclicity Problems
• Time-Reversibility in 2-Dimensional Systems
• Reversing symmetries in dynamical systems
• Reversible Diffeomorphisms and Flows
• The center-focus problem and reversibility

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