Cycles of two-dimensional systems: computer calculations, proofs, and experiments

DOI10.3103/S1063454108030047zbMath1251.93095OpenAlexW1998821148WikidataQ109716949 ScholiaQ109716949MaRDI QIDQ1759537

Elena V. Kudryashova, Gennady Alekseevich Leonov, Nikolay V. Kuznetsov

Publication date: 21 November 2012

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

Full work available at URL: https://doi.org/10.3103/s1063454108030047

zbMATH Keywords

symbolic computingLyapunov's first and second quantitiesneighborhood of equilibrium

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Control problems involving ordinary differential equations (34H05) Control/observation systems governed by ordinary differential equations (93C15)

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Efficient methods in the search for periodic oscillations in dynamical systems ⋮ A criterion for the existence of four limit cycles in quadratic systems ⋮ Analytical research of the Hopf bifurcation in the problem of motion of the rattleback ⋮ Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation ⋮ Visualization of four normal size limit cycles in two-dimensional polynomial quadratic system ⋮ Limit cycles of quadratic systems with a perturbed weak focus of order 3 and a saddle equilibrium at infinity ⋮ Visualization of four limit cycles of two-dimensional quadratic systems in the parameter space ⋮ On the method of harmonic linearization

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