Approach to the chaotic synchronized state of some driving methods

The aim of the present work is to analyze the approach to the asymptotic synchronized state of two different methods of coupling nonlinear systems exhibiting chaotic behavior through driving, namely, the Pecora-Carroll method [Phys. Rev. Lett. 64, 821 (1990)] and a recently introduced modification to this method [Phys. Rev. E 52, R2145 (1995)]. The stability of the different connections can be discussed in terms of the corresponding transverse Lyapunov exponents. In addition, further information can be obtained by studying the local stability of the dynamics of the differences between the two coupled systems. The main behaviors found for these systems are illustrated by using suitable models.