Visualization of four normal size limit cycles in two-dimensional polynomial quadratic system

DOI10.1007/s12591-012-0118-6zbMath1260.34058OpenAlexW2065622633WikidataQ109649631 ScholiaQ109649631MaRDI QIDQ1936723

Nikolay V. Kuznetsov, O. A. Kuznetsova, Gennady Alekseevich Leonov

Publication date: 6 February 2013

Published in: Differential Equations and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12591-012-0118-6

zbMATH Keywords

visualizationlimit cyclequadratic system16th Hilbert problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

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Cites Work

• Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
• Localization of hidden Chua's attractors
• Four limit cycles in quadratic two-dimensional systems with a perturbed first-order weak focus
• Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation
• Limit cycles of quadratic systems with a perturbed weak focus of order 3 and a saddle equilibrium at infinity
• A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems
• Limit cycles of differential equations
• Quadratic vector fields with a weak focus of third order
• Cycles of two-dimensional systems: computer calculations, proofs, and experiments
• Qualitative theory of planar differential systems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Unnamed Item
• Unnamed Item

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