Global Phase Portraits of Kukles Differential Systems with Homogeneous Polynomial Nonlinearities of Degree 6 Having a Center and Their Small Limit Cycles

DOI10.1142/S0218127416500449zbMath1336.34048OpenAlexW2324124483MaRDI QIDQ2806167

Maurício Fronza da Silva, Jaume Llibre

Publication date: 17 May 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500449

zbMATH Keywords

centeraveragingpolynomial vector fieldsPoincaré diskKukles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Averaging method for ordinary differential equations (34C29)

Related Items (5)

An algorithmic approach to small limit cycles of nonlinear differential systems: the averaging method revisited ⋮ Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line ⋮ Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials ⋮ The centers and their cyclicity for a class of polynomial differential systems of degree 7 ⋮ Centers and Limit Cycles of Generalized Kukles Polynomial Differential Systems: Phase Portraits and Limit Cycles

Cites Work

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• Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin
• Global phase portraits of Kukles differential systems with homogeneous polynomial nonlinearities of degree 5 having a center
• Bifurcation of limit cycles by perturbing a class of hyper-elliptic Hamiltonian systems of degree five
• The classification of reversible cubic systems with center
• ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
• Centers for the Kukles homogeneous systems with odd degree
• Averaging methods in nonlinear dynamical systems

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