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ESTIMATING THE DOMAIN OF ATTRACTION VIA MOMENT MATRICES

  • Published : 2009.11.30

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

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Cited by

  1. Enlarging the guaranteed region of attraction in nonlinear systems with bounded parametric uncertainty vol.14, pp.3, 2013, https://doi.org/10.1631/jzus.C1200213
  2. Domain of Attraction Estimation for SIRS Epidemic Models via Sum-of-Square Optimization⋆ vol.44, pp.1, 2011, https://doi.org/10.3182/20110828-6-IT-1002.00947
  3. Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model vol.87, pp.2, 2017, https://doi.org/10.1007/s11071-016-3092-7
  4. THE DOMAIN OF ATTRACTION FOR A SEIR EPIDEMIC MODEL BASED ON SUM OF SQUARE OPTIMIZATION vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.517