Projective synchronization in three-dimensional chaotic systems

In partially linear systems, such as the Lorenz model, chaotic synchronizat ion is possible in only some of the variables. We show that, for the nonsyn chronizing variable, synchronization up to a scale factor is possible. We e xplain the mechanism for this projective form of chaotic synchronization in three-dimensional systems. Projective synchronization is illustrated for t he Lorenz and disk dynamo systems. We also introduce a vector field that ca n be used to predict the scaling factor. [S0031-9007(99)08897-3].