Sign and stability of equilibria in quasi-monotone positive nonlinear systems

The paper deals with the problem of finding the extension of a well-established connection between sign and stability of nontrivial equilibria in positive linear systems to the class of quasi-monotone positive nonlinear systems. The mathematical framework to provide the sufficient conditions guaranteeing such a relationship is the stability theory for nonlinear systems, especially the comparison principles and the method of vector Lyapunov functions. As an illustration of our results we present an example of a double-effect evaporator to study the sign-stability property of its only equilibrium point.