Limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method

DOI10.1016/j.cam.2007.09.007zbMath1362.34049OpenAlexW2053988786MaRDI QIDQ939566

Jinlong Cao

Publication date: 22 August 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2007.09.007

zbMATH Keywords

limit cyclesHopf bifurcationaveraging methodLiapunov constant

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) Averaging method for ordinary differential equations (34C29) 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 (4)

Existence and uniqueness of the exponentially stable limit cycle for a class of nonlinear systems via time-domain approach with differential inequality ⋮ Limit cycles of continuous and discontinuous piecewise-linear differential systems in \(\mathbb{R}^3\) ⋮ Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities ⋮ Bifurcations and distribution of limit cycles which appear from two nests of periodic orbits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
• Bifurcation of limit cycles from quadratic isochrones
• Limit cycles of cubic polynomial vector fields via the averaging theory
• A quartic system and a quintic system with fine focus of order 18
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A method of constructing cycles without contact around a weak focus
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Cubic systems and Abel equations
• On the shape of limit cycles that bifurcate from Hamiltonian centers
• Limit cycles bifurcating from a \(k\)-dimensional isochronous center contained in \(\mathbb R^n\) with \(k\leqslant n\)
• The number of limit cycles of certain polynomial differential equations
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• Integrable systems in the plane with center type linear part
• On the nonexistence, existence and uniqueness of limit cycles
• On a certain generalization of Bautin's theorem
• Algorithmic Derivation of Centre Conditions
• Averaging methods in nonlinear dynamical systems
• The shape of limit cycles that bifurcate from non-Hamiltonian centers
• The multiplicity of zero and limit cycles for Abel equations
• Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

This page was built for publication: Limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method