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International Conference on Computer Aided Systems Theory

EUROCAST 1995: Computer Aided Systems Theory — EUROCAST '95 pp 137–150Cite as

Basins of attraction estimation through symbolic graphical computing techniques

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Part of the book series: Lecture Notes in Computer Science ((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.

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References

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Authors and Affiliations

  1. Facultad de Ingenieria Escuela de Sistemas - Dept. de Sislemas de Control, Universidad de Los Andes, Apartado 11, 5251-A, La Hechicera, Mérida, Venezuela

    Jesús Rodríguez-Millán

Authors
  1. Jesús Rodríguez-Millán
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Editor information

Franz Pichler Roberto Moreno Díaz Rudolf Albrecht

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© 1996 Springer-Verlag Berlin Heidelberg

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Rodríguez-Millán, J. (1996). Basins of attraction estimation through symbolic graphical computing techniques. In: Pichler, F., Díaz, R.M., Albrecht, R. (eds) Computer Aided Systems Theory — EUROCAST '95. EUROCAST 1995. Lecture Notes in Computer Science, vol 1030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034756

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  • DOI: https://doi.org/10.1007/BFb0034756

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60748-9

  • Online ISBN: 978-3-540-49358-7

  • eBook Packages: Springer Book Archive

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