Relationship between Stability and Connectedness of Non-linear Systems

Abstract

Gardner and Ashby1 have studied the relation between the probability of stability p(S) and the extent of connectedness (“connectance”) C of large linear dynamical systems. They found a very interesting on–off-type (numerical) result: for reasonably large systems (number of components n ≥ 10) there is a critical value, Cc of C, below which the system is almost certainly stable, but above which it becomes almost certainly unstable.