The stability boundary of synchronized states in globally coupled dynamical systems

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