On integrability conditions and limit cycle bifurcations for polynomial systems

DOI10.1016/j.amc.2015.04.019zbMath1410.34114OpenAlexW220881879MaRDI QIDQ1663555

Brigita Ferčec

Publication date: 21 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.04.019

zbMATH Keywords

integrabilitylimit cyclecenter varietycyclicity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (1)

Dynamical analysis of a two prey-one predator system with quadratic self interaction

Uses Software

• SINGULAR
• primdec

Cites Work

• An approach to solving systems of polynomials via modular arithmetics with applications
• Limit cycles of differential equations
• Integrability conditions for Lotka-Volterra planar complex quintic systems
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• Integrability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities
• Evaluating cyclicity of cubic systems with algorithms of computational algebra
• Stability of motion
• The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System
• The Center and Cyclicity Problems
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