A computational approach for studying domains of attraction for nonlinear systems
type: Item
instance of: scholarly article
title: A computational approach for studying domains of attraction for nonlinear systems
zbMATH Open document ID: 0655.70019
DOI: 10.1016/0020-7462(88)90026-1
published in: International Journal of Non-Linear Mechanics
publication date: 1988-01-01T00:00:00Z
review text: The determination of the domains of attraction of equilibrium states and of periodic solutions plays an important role in delineating the global behavior of nonlinear dynamical systems. In this paper, we propose a computational scheme of backward mappings for obtaining the global domains of attraction. The approach is based on the Lyapunov theory and extends a method proposed by \textit{C. S. Hsu} [Adv. Appl. Mech. 17, 245- 301 (1977; Zbl 0472.70022)] for discrete time systems. The method consists of an interative procedure to be applied to asymptotically stable equilibrium states and stable periodic solutions and converges to the total domain of attraction of the given solution. The computational scheme proposed here is applicable to both time-invariant and periodic, continuous-time dynamical systems as well as discrete-time dynamical systems. In the paper the mathematical basis for the approach and the computational algorithm are described. The usefulness of the method is illustrated by applying it to different classes of dynamical systems. The study indicates that the method is efficient in analyzing the global behavior of multidimensional systems, both time-invariant and time varying.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 4070406
zbMATH Keywords: domains of attraction of equilibrium states
zbMATH Keywords: periodic solutions
zbMATH Keywords: nonlinear dynamical systems
zbMATH Keywords: computational scheme of backward mappings
zbMATH Keywords: global domains of attraction
zbMATH Keywords: asymptotically stable equilibrium states
zbMATH Keywords: stable periodic solutions
author: Henryk Flashner
author: Ramesh S. Guttalu
MaRDI profile type: Publication
full work available at URL: 0020-7462(88)90026-1
OpenAlex ID: W2000803546
description: scientific article; zbMATH DE number 4070406