Limit cycles of some polynomial differential systems in dimension 2, 3 and 4, via averaging theory

DOI10.1080/00036810701556136zbMath1362.34047OpenAlexW2059317923MaRDI QIDQ5457912

Jaume Llibre, Marco Antonio Teixeira, Anna Cima

Publication date: 10 April 2008

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810701556136

zbMATH Keywords

limit cyclesynchronizationaveraging methodpolynomial differential systemlinear center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Degree theory for nonlinear operators (47H11) Perturbations of ordinary differential equations (34D10) 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 (15)

Limit cycles of polynomial differential systems bifurcating from the periodic orbits of a linear differential system in \(\mathbb R^d\) ⋮ Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems ⋮ Bifurcation of multiple periodic solutions for a class of nonlinear dynamical systems in \((m+4)\)-dimension ⋮ Periodic orbits for perturbations of piecewise linear systems ⋮ Melnikov theory for a class of planar hybrid systems ⋮ Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces ⋮ Periodic orbits and invariant cones in three-dimensional piecewise linear systems ⋮ Limit cycles for the class of \(D\)-dimensional polynomial differential systems ⋮ Limit cycles for a class of three-dimensional polynomial differential systems ⋮ Periodic orbits in analytically perturbed Poisson systems ⋮ Periodic orbits for perturbed non-autonomous differential equations ⋮ Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application ⋮ Bifurcation and number of subharmonic solutions of a 4D non-autonomous slow-fast system and its application ⋮ Perturbations of parallel flows on the sphere in \(\mathbb R^3\) ⋮ Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+ 2)–dimension

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Averaging methods for finding periodic orbits via Brouwer degree.
• Limit cycles for multidimensional vector fields. The elliptic case
• Applications of robust synchronization to communication systems
• An averaging method for Hamiltonian systems, exponentially close to integrable ones
• Limit cycles of three-dimensional polynomial vector fields
• Limit cycles appearing after perturbation of certain multidimensional vector fields.

This page was built for publication: Limit cycles of some polynomial differential systems in dimension 2, 3 and 4, via averaging theory