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Zbl 0786.34033
Li, Yi; Muldowney, James S.
On Bendixson's criterion. (English)
[J] J. Differ. Equations 106, No.1, 27-39 (1993). ISSN 0022-0396

Summary: For autonomous differential equations in $\bbfR\sp n$ criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories. The technique is based on the study of functionals on 2-surfaces. Results generalize to higher dimensions a criterion of Bendixson for the non-existence of nonconstant periodic solutions in the case $n=2$. As an example, an application to the Lorenz system in $\bbfR\sp 3$ is given.

MSC 2000:: *34C05 Qualitative theory of some special solutions of ODE

Keywords: autonomous differential equations; existence of invariant closed curves; periodic or homoclinic trajectories; criterion of Bendixson; periodic solutions; Lorenz system

Cited in: Zbl 1224.34230 Zbl 1198.34097 Zbl 1142.34370 Zbl 1100.92015 Zbl 1144.34373 Zbl 1042.34075 Zbl 1091.34037 Zbl 1009.34062

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