Necessary conditions for a limit cycle and its basin of attraction.

DOI10.1016/j.na.2003.07.020zbMath1048.34064OpenAlexW2086549513MaRDI QIDQ1426417

Peter Giesl

Publication date: 14 March 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.07.020

zbMATH Keywords

Periodic orbitDynamical systemBasin of attractionAutonomous ordinary differential equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Attractors of solutions to ordinary differential equations (34D45)

Related Items

Borg's criterion for almost periodic differential equations ⋮ On the determination of the basin of attraction of a periodic orbit in two-dimensional systems ⋮ Construction of a CPA contraction metric for periodic orbits using semidefinite optimization ⋮ Areas of attraction for nonautonomous differential equations on finite time intervals ⋮ Finding positively invariant sets and proving exponential stability of limit cycles using sum-of-squares decompositions ⋮ On limiting properties of Lyapunov asymptotically stable and Zhukovsky asymptotically rigid trajectories of a dynamic system ⋮ Converse theorems on contraction metrics for an equilibrium ⋮ Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation ⋮ On a matrix-valued PDE characterizing a contraction metric for a periodic orbit ⋮ On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems ⋮ Computation of a Contraction Metric for a Periodic Orbit Using Meshfree Collocation ⋮ Review on computational methods for Lyapunov functions

Cites Work

• Local instability and localization of attractors. From stochastic generator to Chua's systems
• On Global Asymptotic Stability of Solutions of Differential Equations
• Dynamical Systems with a Certain Local Contraction Property.
• Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization
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