On the property sign-stability of equilibria in quasimonotone positive nonlinear systems

This paper deals with the problem of generalizing the relationship existing between sign and stability of non-trivial equilibria in positive linear systems to the class of quasimonotone positive nonlinear systems. Such a class of positive systems is founded in many mathematical models of physical processes. The mathematical tools which enable us to obtain the sufficient conditions, guaranteeing the equivalence sign-stability, are the so-called Matrosov´s comparison principle and the Lyapunov vector function method. The results are used to study the property sign-stability of the only equilibrium point in a bilinear model of a double effect evaporator