Remarks on the invalidation of biological models using monotone systems theory

Cooperative systems, and more generally systems with sign-definite interactions between variables, are an important class of models in several domains of applications, and in particular in molecular biology. The goal of this paper is to present techniques for finding out what type of solutions are compatible with a given sign pattern of interactions among state/input variables, once the input behaviour is also known. By ``type'' of solutions we mean the sequence of upwards or downwards segments that variables can exhibit (essentially sign-patterns derivatives of variables) once input profiles are also specified.