Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation

DOI10.1134/S1560354710020218zbMath1209.34041OpenAlexW2013802952MaRDI QIDQ618214

O. A. Kuznetsova, Gennady Alekseevich Leonov

Publication date: 14 January 2011

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354710020218

zbMATH Keywords

Liénard systemsymbolic computationquadratic systemLyapunov quantitiesHilbert's 16-th problemlocalization of limit cyclessmall and large limit cycles

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) 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)

Related Items (8)

Visualization of four normal size limit cycles in two-dimensional polynomial quadratic system ⋮ Hidden attractors in dynamical systems ⋮ Visualization of four limit cycles of two-dimensional quadratic systems in the parameter space ⋮ Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits ⋮ Unnamed Item ⋮ Bifurcation analysis and dynamic behaviour of an inverted pendulum with bounded control ⋮ Bifurcations of limit cycles in complex networks of Hamiltonian systems and Lloyd's conjecture ⋮ Analytical-Numerical Methods for Hidden Attractors’ Localization: The 16th Hilbert Problem, Aizerman and Kalman Conjectures, and Chua Circuits

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