Basins of attraction of invariant regular manifolds

In this work, we present a new approach for the determination of the stability properties of regular invariant surfaces in the phase space of a system of ordinary differential equations. This approach also yields an estimation for basin of attraction of the invariant surface. The stability problem is reduced to the study of a system of non-autonomous linear differential equations and the use of the Wasewski's inequalities. We illustrate our method for a system of equations describing the generalized mass action (GMA) model for biochemical reactions.