Stability properties of a general class of nonlinear dynamical systems

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear syste ms, the so-called quasi-polynomial vector fields, with the help of a natura l embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such cond itions. We apply our method to obtain new results for LV systems, by a repa rametrization in time variable, and to study general nonlinear vector field s, originally far from the LV format.