Synchronization of simple chaotic flows

Nonlinear scalar third-order differential equation or jerky dynamics (x) tr iple over dot = J(x, (x) over dot, (x) double over dot) have recently attra cted considerable interest since they constitute an important tool to ident ify and classify elementary chaotic flows. We investigate whether and under what conditions such systems can be synchronized by various coupling schem es such as the methods of Pecora-Carroll and Cuomo-Oppenheim, BK-coupling a nd active-passive decomposition. In particular, for the latter two schemes, we present specific, simplified coupling or decomposition approaches that allow for analytical estimates of the rapidity of the synchronization error . (C) 2001 Elsevier Science B.V. All rights reserved.