In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems fo...In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems for the global topological classification of Q(x). They derivethe necessary and sufficient conditions for the global asymptotic stability and the boundednessof vector field Q(x), and obtain the criterion for the global topological equivalence of twohomogeneous vector fields.展开更多
文摘In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems for the global topological classification of Q(x). They derivethe necessary and sufficient conditions for the global asymptotic stability and the boundednessof vector field Q(x), and obtain the criterion for the global topological equivalence of twohomogeneous vector fields.
