The paper deals with the system \[ \begin{gathered} \dot x = f(x),\quad x\in \mathbb{R}^n,\\ f\in C^1(\mathbb{R}^n,\mathbb{R}^n),\quad f(0) = 0. \end{gathered}\tag{1} \] For system (1) the authors consider homogeneous density functions for proving global attractivity of the zero equilibrium in a homogeneous system. It is shown that the existence of such a function is guaranteed when the equilibrium is asymptotically stable or, in the more general case, when there exists a nonhomogeneous density function for the same system satisfying some reasonable conditions.
For the entire collection see [Zbl 1005.00024].