Geometrical conditions for the stability of orbits in planar systems
1996 ◽
Vol 120
(3)
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pp. 499-519
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Keyword(s):
The Real
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AbstractGiven a vector field X on the real plane, we study the influence of the curvature of the orbits of ẋ = X┴(x) in the stability of those of the system x˙ = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the general case, we also provide expressions for the first three derivatives of the Poincaré map associated to a periodic orbit in terms of geometrical quantities.
2018 ◽
Vol 11
(05)
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pp. 1850071
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2015 ◽
Vol 08
(03)
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pp. 1550030
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2020 ◽
Vol 2020
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pp. 1-12
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2017 ◽
Vol 82
(5)
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pp. 945-970
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2013 ◽
Vol 791-793
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pp. 1322-1327
2007 ◽
Vol 8
(3)
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pp. 191-203
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2005 ◽
Vol 15
(04)
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pp. 1253-1265
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2010 ◽
Vol 03
(03)
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pp. 299-312
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2018 ◽
Vol 15
(1)
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pp. 36-47
Keyword(s):