Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2009; 46(6): 1237-1248

Printed November 1, 2009

https://doi.org/10.4134/BKMS.2009.46.6.1237

Copyright © The Korean Mathematical Society.

Estimating the domain of attraction via moment matrices

Chunji Li, Cheon Seoung Ryoo, Ning Li, and Lili Cao

Northeastern University, Hannam University, Northeastern University, and Northeastern University

Abstract

The domain of attraction of a nonlinear differential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.

Keywords: domain of attraction, moment matrices, Lyapunov function, SIRS model

MSC numbers: 37C75, 44A60