Global dynamics of a SD oscillator

DOI10.1007/S11071-017-3979-YzbMath1390.34119OpenAlexW2775656422MaRDI QIDQ1649949

Jaume Llibre, Hebai Chen, Yilei Tang

Publication date: 29 June 2018

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/199336

zbMATH Keywords

limit cycleHopf bifurcationaveraging methodhomoclinic loopBogdanov-Takens bifurcationSD oscillator

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Degree theory for nonlinear operators (47H11) Averaging method for ordinary differential equations (34C29)

Related Items (13)

Existence and stability of periodic oscillations of a smooth and discontinuous oscillator ⋮ The discontinuous limit case of an archetypal oscillator with a constant excitation and van der Pol damping ⋮ STRANGE NONCHAOTIC ATTRACTORS IN A QUASIPERIODICALLY FORCED ARTICULATED MOORING TOWER MODEL ⋮ An oscillator with two discontinuous lines and Van der Pol damping ⋮ A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation ⋮ Bursting oscillations of the perturbed quasi-zero stiffness system with positive/negative stiffness at origin ⋮ Global dynamics of a Filippov system with general parameters and saddle structure of a regular-SN ⋮ Proof of Artés-Llibre-Valls's conjectures for the Higgins-Selkov and the Selkov systems ⋮ The Poincaré bifurcation of a SD oscillator ⋮ Periodic orbits of linear Filippov systems with a line of discontinuity ⋮ Phase portraits of the Higgins-Selkov system ⋮ Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications ⋮ Mechanisms of strange nonchaotic attractors in a nonsmooth system with border-collision bifurcations

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• Cubic Lienard equations with linear damping
• Generalized normal sectors and orbits in exceptional directions
• Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics

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