On Homogeneous Density Functions

We consider homogeneous density functions for proving almost globalattractivity of the zero equilibrium in a homogeneous system. It is shownthat the existence of such a function is guaranteed whenthe equilibrium is asymptotically stable, or in the more general case, whenthere exists a nonhomogeneous density function for the same systemsatisfying some reasonable conditions. Results related to robustness under nonhomogenizing perturbationsare also presented