Computing the number, location and stability of fixed points of Poincare maps

Author

Fujisaka, Hisato ; Sato, Chikara

Author_Institution

Dept. of Instrum. Eng., Keio Univ., Yokohama, Japan

Volume

44

Issue

4

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

303

Lastpage

311

Abstract

A numerical method is presented to compute the number of fixed points of Poincare maps of either autonomous or nonautonomous ordinary differential equations. The method consists of three concepts: the Poincare map, the second map constructed from the Poincare map, and topological degree. The topological degree calculated from the second map is equal to the number of fixed points of the Poincare map in a given domain of a Poincare section. Thus the computation procedure is simply to compute the topological degree of the second map. The combined use of this method and Newton´s iterative method gives the location and stability of all the fixed points in the domain

Keywords

Newton method; Poincare mapping; circuit stability; network topology; nonlinear network analysis; Newton´s iterative method; Poincare maps; computation procedure; fixed points; nonlinear network analysis; stability; topological degree; Circuit stability; Convergence of numerical methods; Differential equations; Electronic circuits; Iterative methods; Life members; Nonlinear dynamical systems; Nonlinear equations; Optical fiber communication; Orbits;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.563620

Filename

563620