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On the basin of attraction of dissipative planar vector fields

Part of the Lecture Notes in Mathematics book series (LNM,volume 1455)

Abstract

An estimate for the size of the basin of attraction of an equilibrium point for a class of planar dissipative vector fields is given here. Our main result, which generalizes a theorem of Krasowskii, is applied to give several sufficient conditions for global asymptotic stability.

Partially supported by CIGYT grant number PB86-0351.

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References

  1. Gasull, A., Llibre, J. and Sotomayor, J., Global asymptotic stability of differential equations in the plane, to appear in J. of Diff. Equations, 1990.

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  2. Hartman, P. and Olech, C., On global asymptotic stability of differential equations, Trans. Amer. Math. Soc. 104 (1962), 159–178.

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  3. Krasowskii, N.N., On the behaviour in the large of the integral curves of a system of two differential equations, Prikl. Mat. Mek. 18 (1954), 149–154. (in russian).

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  4. Krasowskii, N.N., Stability of Motion, Stanford University Press, Stanford, California 1963.

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  5. Olech, C., On the global stability of an autonomous system on the plane, Cont. to Diff. Eq. 1 (1963), 389–400.

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© 1990 Springer-Verlag

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Gasull, A., Sotomayor, J. (1990). On the basin of attraction of dissipative planar vector fields. In: Françoise, JP., Roussarie, R. (eds) Bifurcations of Planar Vector Fields. Lecture Notes in Mathematics, vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085393

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  • DOI: https://doi.org/10.1007/BFb0085393

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53509-6

  • Online ISBN: 978-3-540-46722-9

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