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Basins of attraction estimation through symbolic graphical computing techniques

  • Jesús Rodríguez-Millán
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1030)

Abstract

In the present paper an elementary symbolic method for the estimation of basins of attraction in second order nonlinear dynamical systems is formulated and its implementation using Mathematica® is shown. The estimation algorithm is based upon the construction of positively invariant compact boxes that trap the trajectories with unbounded initial conditions. We obtain such boxes through a Lyapunov function whose orbital derivative is bounded by a bounding function that can be represented as the addition of two scalar functions. The detection of persistent oscillating behaviors deserves a prominent place between all possible applications of our tool, as it will be shown by considering Fitzhugh Equations as a case study.

Keywords

Dissipative Dynamical Systems Basins of Attraction Lyapunov Functions Nonlinear Oscillations Symbolic Computing 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jesús Rodríguez-Millán
    • 1
  1. 1.Facultad de Ingenieria Escuela de Sistemas - Dept. de Sislemas de ControlUniversidad de Los AndesLa HechiceraVenezuela

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