A computational approach for studying domains of attraction for nonlinear systems
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.
domains of attraction of equilibrium states
computational scheme of backward mappings
asymptotically stable equilibrium states
scientific article; zbMATH DE number 4070406