Global asymptotic stability for differentiable vector fields of R2
نویسندگان
چکیده
منابع مشابه
Asymptotic Stability at Infinity for Differentiable Vector Fields of the Plane
Let X : R\Dσ → R 2 be a differentiable (but not necessarily C) vector field, where σ > 0 and Dσ = { z ∈ R : ‖z‖ ≤ σ } . If for some ǫ > 0 and for all p ∈ R\Dσ, no eigenvalue of DpX belongs to (−ǫ, 0] ∪ {z ∈ C : R(z) ≥ 0}, then a) For all p ∈ R\Dσ, there is a unique positive semi–trajectory of X starting at p; b) I(X), the index of X at infinity, is a well defined number of the extended real lin...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2004
ISSN: 0022-0396
DOI: 10.1016/j.jde.2004.04.015