On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems

DOI10.1016/j.jmaa.2009.01.027zbMath1173.34034OpenAlexW1974810735MaRDI QIDQ1018317

Peter Giesl

Publication date: 19 May 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.01.027

zbMATH Keywords

Lyapunov functionbasin of attractionordinary differential equationperiodic orbitradial basis functionmeshless collocation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items

Construction of a CPA contraction metric for periodic orbits using semidefinite optimization ⋮ Review on contraction analysis and computation of contraction metrics ⋮ A novel moving orthonormal coordinate-based approach for region of attraction analysis of limit cycles ⋮ Converse theorems on contraction metrics for an equilibrium ⋮ Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation ⋮ Optimizing the stable behavior of parameter-dependent dynamical systems -- maximal domains of attraction, minimal absorption times ⋮ Review on computational methods for Lyapunov functions

Cites Work

• Unnamed Item
• Construction of global Lyapunov functions using radial basis functions
• On the basin of attraction of limit cycles in periodic differential equations
• Necessary conditions for a limit cycle and its basin of attraction.
• A constructive converse Lyapunov theorem on exponential stability
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Nonlinear autonomous oscillations. Analytical theory
• On the determination of the basin of attraction of a periodic orbit in two-dimensional systems
• Meshless Collocation: Error Estimates with Application to Dynamical Systems
• Dynamical Systems with a Certain Local Contraction Property.
• Scattered Data Approximation

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