On the limit cycles of planar autonomous systems

DOI10.1142/S0252959901000310zbMath0996.34026OpenAlexW2357950133MaRDI QIDQ5943617

Tifei Qian, Mao'an Han

Publication date: 28 October 2002

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0252959901000310

zbMATH Keywords

Lyapunov functionlimit cyclebifurcationsBendixson-Dulac criterionplanar ordinary differential equation

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) 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) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (3)

Global bifurcation of a perturbed double-homoclinic loop ⋮ THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER CUBIC PERTURBATIONS ⋮ THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER POLYNOMIAL PERTURBATIONS

Cites Work

• On the nonexistence, existence and uniqueness of limit cycles
• Boundedness of solutions and existence of limit cycles for a nonlinear system
• Periodic solutions of generalized Liénard equations

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