Contraction analysis of virtually positive systems

Stability analysis methodologies tailored for positive linear systems have been generalized to cooperative nonlinear systems. However, some network systems, such as epidemic dynamics characterized by susceptible–infected–susceptible models, are not cooperative. To apply the tools originally developed this class of non-cooperative in paper, we propose concept virtual positivity a generalization cooperativity. Non-cooperative (or even non-monotone) can be virtually positive. As main result, extend contraction conditions Particularly, derive necessary and sufficient incremental exponential stability (IES). Also, show that IES system implies original if has an equilibrium point property.