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Basins of attraction of invariant regular manifolds

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  • Figueiredo, Annibal
  • Rocha Filho, Tarcisio M.

Abstract

In this work, we present a new approach for the determination of the stability properties of regular invariant surfaces in the phase space of a system of ordinary differential equations. This approach also yields an estimation for basin of attraction of the invariant surface. The stability problem is reduced to the study of a system of non-autonomous linear differential equations and the use of the Wasewski’s inequalities. We illustrate our method for a system of equations describing the generalized mass action (GMA) model for biochemical reactions.

Suggested Citation

  • Figueiredo, Annibal & Rocha Filho, Tarcisio M., 2009. "Basins of attraction of invariant regular manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1877-1889.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1877-1889
    DOI: 10.1016/j.chaos.2007.09.070
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    References listed on IDEAS

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    1. Figueiredo, A. & Filho, T.M.Rocha & Brenig, L., 1999. "Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka–Volterra systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 158-180.
    2. de Souza, S.L.T. & Caldas, I.L. & Viana, R.L. & Balthazar, J.M. & Brasil, R.M.L.R.F., 2005. "Basins of attraction changes by amplitude constraining of oscillators with limited power supply," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1211-1220.
    3. Liu, Zengrong & Li, Ying & Chen, Guanrong, 2007. "The basin of attraction of the Chen attractor," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1696-1703.
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    1. Marão, José & Liu, Xinzhi & Figueiredo, Annibal, 2012. "Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1067-1079.

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