Estimating region of attraction for polynomial vector fields by homotopy methods

Despite the prevalence of synchronization analysis on complex dynamical networks, little attention was paid to the problem of estimating their regions of attraction. This paper addresses the issue of estimating the region of attraction of an equilibrium ...

Given a complex polynomial p(z) with at least three distinct roots, we first prove that no rational iteration function exists where the basin of attraction of a root coincides with its Voronoi cell. In spite of this negative result, we prove that the ...

Vertex- and face-based subdivision schemes are now routinely used in geometric modeling and computational science, and their primal/dual relationships are well studied. In this paper, we interpret these schemes as defining bases for discrete ...