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An index theorem and Bendixson's negative criterion for certain differential equations of higher dimension

Published online by Cambridge University Press:  14 November 2011

Russell A. Smith
Russell A. Smith
Affiliation:
Department of Mathematics, University of Durham
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Synopsis

Poincaré's theorem on the sum of the indices of a plane autonomous differential equation at its critical points inside a periodic orbit is here extended to the periodic orbits of higher-dimensional equations under certain conditions. Under the same conditions, higher-dimensional extensions are obtained of some theorems of Bendixson and others which exclude periodic orbits from regions in which the differential equation haspositive divergence. The application of these results to feedback control equations is also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 63 - 77
Copyright
Copyright © Royal Society of Edinburgh 1981

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