On the dynamics of the Rayleigh-Duffing oscillator

DOI10.1016/J.NONRWA.2018.07.007zbMath1415.34059OpenAlexW2883925788WikidataQ129482011 ScholiaQ129482011MaRDI QIDQ1729164

Jaume Giné, Claudia Valls

Publication date: 27 February 2019

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2018.07.007

zbMATH Keywords

first integralscenter problemRayleigh-Duffing oscillator

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) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

On linearizability via nonlocal transformations and first integrals for second-order ordinary differential equations ⋮ Integrability analysis of Muthuswamy-Chua-Ginoux system ⋮ On an integrability criterion for a family of cubic oscillators ⋮ Unnamed Item ⋮ Chaos of the Rayleigh-Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation ⋮ Dynamics of polynomial Rayleigh-Duffing system near infinity and its global phase portraits with a center ⋮ The focus case of a nonsmooth Rayleigh-Duffing oscillator ⋮ The Coexisting Behaviors on the Boundary of a Duffing-like Oscillator with Signum Nonlinearity and Its FPGA-Based Implementation ⋮ Linearizability conditions for the Rayleigh-like oscillators ⋮ Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane ⋮ Liouvillian integrability of a general Rayleigh-Duffing oscillator ⋮ Darboux first integrals and linearizability of quadratic-quintic Duffing-van der Pol oscillators ⋮ Darboux integrability of a Mathieu-van der Pol-Duffing oscillator

Cites Work

• Unnamed Item
• Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator
• Essential variables in the integrability problem of planar vector fields
• On some open problems in planar differential systems and Hilbert's 16th problem
• Qualitative theory of planar differential systems
• On the differentiability of first integrals of two dimensional flows
• Global study of Rayleigh–Duffing oscillators
• Liouvillian First Integrals of Differential Equations
• The Bianchi VIII model is neither global analytic nor Darboux integrable

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