Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities

DOI10.1016/j.jde.2018.05.019zbMath1405.34027OpenAlexW2803987287MaRDI QIDQ1671209

Jianfeng Huang, Haihua Liang, Jaume Llibre

Publication date: 6 September 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/199335

zbMATH Keywords

limit cyclespolynomial differential systemshomogeneous nonlinearitiesnon-existence and uniqueness

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (16)

On the uniqueness of limit cycles for generalized Liénard systems ⋮ Global planar dynamics with a star node and contracting nonlinearity ⋮ On the Number of Limit Cycles Bifurcating from a Compound Polycycle ⋮ Periodic orbits in piecewise Riccati vector fields ⋮ Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems ⋮ Upper bounds of limit cycles in Abel differential equations with invariant curves ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ Global dynamics of hybrid van der Pol-Rayleigh oscillators ⋮ Planar systems and Abel equations ⋮ BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES ⋮ A new Chebyshev criterion and its application to planar differential systems ⋮ On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique ⋮ Criteria on the existence of limit cycles in planar polynomial differential systems ⋮ On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones

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