Existence criteria for cycles in two-dimensional quadratic systems

DOI10.3103/S1063454107030028zbMath1161.34017OpenAlexW2092334626MaRDI QIDQ946002

Gennady Alekseevich Leonov

Publication date: 22 September 2008

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1063454107030028

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Visualization of four limit cycles of two-dimensional quadratic systems in the parameter space ⋮ Cycles of two-dimensional systems: computer calculations, proofs, and experiments

Cites Work

• Unnamed Item
• Extrema of the Andronov-Hopf function of a polynomial Lienard system
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• Centennial History of Hilbert's 16th Problem

This page was built for publication: Existence criteria for cycles in two-dimensional quadratic systems