SIGN AND STABILITY OF EQUILIBRIA IN QUASI-MONOTONE POSITIVE NONLINEAR-SYSTEMS

The paper deals with the problem of finding the extension of a well-es tablished connection between sign and stability of nontrivial equilibr ia in positive linear systems to the class of quasi-monotone positive nonlinear systems. The mathematical framework to provide the sufficien t conditions guaranteeing such a relationship is the stability theory for nonlinear systems, especially the comparison principles and the me thod of vector Lyapunov functions. As an illustration of our results w e present an example of a double-effect evaporator to study the sign-s tability property of its only equilibrium point.