Quadratic Morse-Smale vector fields which are not structurally stable

Chicone, Carmen; Shafer, Douglas S.

doi:10.1090/S0002-9939-1982-0647911-9

Quadratic Morse-Smale vector fields which are not structurally stable
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by Carmen Chicone and Douglas S. Shafer PDF

Proc. Amer. Math. Soc. 85 (1982), 125-134 Request permission

Abstract:

An example is given of a quadratic system in the plane which is Morse-Smale but not structurally stable. Also, it is proved that no such example exists for a quadratic system which is a gradient.

References

Qualitative theory of second-order dynamic systems

Theory of bifurcations of dynamic systems on the plane

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