Limit cycles of cubic polynomial vector fields via the averaging theory
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Publication:875278
DOI10.1016/j.na.2006.02.016zbMath1127.34025OpenAlexW2020278866MaRDI QIDQ875278
Publication date: 13 April 2007
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.na.2006.02.016
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)
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Cites Work
- Bifurcation of limit cycles from quadratic isochrones
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Bifurcations of limit cycles forming compound eyes in the cubic system
- Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
- Averaging methods for finding periodic orbits via Brouwer degree.
- On the shape of limit cycles that bifurcate from Hamiltonian centers
- Abelian integrals for cubic vector fields
- Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop
- Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers
- Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
- Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
- On the nonexistence, existence and uniqueness of limit cycles
- Eleven small limit cycles in a cubic vector field
- Averaging methods in nonlinear dynamical systems
- The shape of limit cycles that bifurcate from non-Hamiltonian centers
- Averaging analysis of a perturbated quadratic center
- Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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