Limit cycles for generalized Kukles polynomial differential systems

DOI10.1016/j.na.2010.09.064zbMath1228.34050OpenAlexW1995064835MaRDI QIDQ622395

Jaume Llibre, Ana Cristina Mereu

Publication date: 31 January 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150453

zbMATH Keywords

limit cycleaveraging theoryKukles systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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)

Related Items (12)

On the limit cycles of a class of Kukles type differential systems ⋮ Bifurcation of limit cycles for a family of perturbed Kukles differential systems ⋮ Unnamed Item ⋮ Maximum number of limit cycles for generalized Kukles differential system ⋮ An estimation for the number of limit cycles in a Liénard-like perturbation of a quadratic nonlinear center ⋮ On the limit cycles of a class of generalized Kukles polynomial differential systems via averaging theory ⋮ Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree ⋮ Periodic orbits for perturbed non-autonomous differential equations ⋮ Maximum number of limit cycles for generalized Kukles polynomial differential systems ⋮ Analytic Integrability of Two Lopsided Systems ⋮ Limit cycles for a class of discontinuous piecewise generalized kukles differential systems ⋮ ON THE LIMIT CYCLES FOR A CLASS OF GENERALIZED KUKLES DIFFERENTIAL SYSTEMS

Cites Work

• Limit cycles for the kukles system
• Bifurcation of limit cycles from quadratic isochrones
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Averaging methods for finding periodic orbits via Brouwer degree.
• Coexistence of limit cycles and invariant algebraic curves for a Kukles system
• Cubic systems of nonlinear oscillations with seven limit cycles
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• On the nonexistence, existence and uniqueness of limit cycles
• Successive derivatives of a first return map, application to the study of quadratic vector fields
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