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http://dx.doi.org/10.4134/BKMS.2009.46.6.1237

ESTIMATING THE DOMAIN OF ATTRACTION VIA MOMENT MATRICES  

Li, Chunji (Institute of System Science College of Sciences Northeastern University)
Ryoo, Cheon-Seoung (Department of Mathematics Hannam University)
Li, Ning (Institute of System Science College of Sciences Northeastern University)
Cao, Lili (Institute of System Science College of Sciences Northeastern University)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.6, 2009 , pp. 1237-1248 More about this Journal
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;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
연도 인용수 순위
1 R. Curto and L. Fialkow, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc. 119 (1996), no. 568, x+52 pp
2 O. Hachicho, A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions, J. Franklin Inst. 344 (2007), no. 5, 535-552   DOI   ScienceOn
3 O. Hachicho and B. Tibken, Estimating domains of attractions of a class of nonlinear dynamical systems with LMI methods based on the theory of moments, Proceedings of the 41st IEEE Conference on Decision and Control, pp. 3150-3155, Las Vegas, USA, 2002
4 Y. Jin, W. Wang, and S. Xiao, An SIRS model with a nonlinear incidence rate, Chaos Solitons Fractals 34 (2007), no. 5, 1482.1497   DOI   ScienceOn
5 X. J. Lan, H. X. Yang, and Z. Q. Sun, Class of the combined SIR and SIS contagion model for population for varying size, J. Chongqing Institute Technology (Natural Science Edition, Chinese) 21 (2007), no. 6, 40-42
6 C. Li, I. B. Jung, and S. S. Park, Complex moment matrices via Halmos-Bram and Embry conditions, J. Korean Math. Soc. 44 (2007), no. 4, 949-970   과학기술학회마을   DOI   ScienceOn
7 C. Li and S. H. Lee, The quartic moment problem, J. Korean Math. Soc. 42 (2005), no. 4, 723-747   과학기술학회마을   DOI   ScienceOn
8 J. Lofberg, Yalmip : A toolbox for modeling and optimization in matlab, in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004   DOI
9 I. B. Jung, E. Ko, C. Li and, S. S. Park, Embry truncated complex moment problem, Linear Algebra Appl. 375 (2003), 95-114   DOI   ScienceOn
10 J. B. Lasserre, Global optimization with polynomials and the problem of moments, SIAM J. Optim. 11 (2001), no. 3, 796-817   DOI   ScienceOn