The stability boundary of synchronized states in globally coupled dynamical systems

The stability boundary of synchronized states in families of globally coupled map lattices and differential equations are studied. It is shown that this boundary may have a very complicated structure in a wide variety of systems. This explains why states can go through sequences of desynchronization and resynchronization as a parameter is varied: in 'typical' systems, between any two parameter values at which synchronized states are unstable there are parameter values at which synchronized states are stable! (C) 1999 Elsevier Science B.V. All rights reserved.