Estimating the domain of attraction via moment matrices
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1237-1248
https://doi.org/10.4134/BKMS.2009.46.6.1237
Published online November 1, 2009
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
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