Bridge the Gap between the Lorenz System and the Chen System

Recently, the study of chaotic dynamics has evolved from the traditional trend of understanding and analyzing chaos to the new intention of controlling and utilizing it [Chen & Dong, 1998; Wang & Chen, 2000; Lü et al., 2002d]. The Lorenz system, found in 1963, produces the best-known canonical chaotic attractor in a simple three-dimensional autonomous system [Lorenz, 1963; Stewart, 2000]. In 1999, Chen found a similar but nonequivalent chaotic attractor [Chen & Ueta, 1999; Ueta & Chen, 2000], which is now known to be the dual of the Lorenz system, in a sense defined in [Vanĕc̆ek & C̆elikovský, 1996]: The Lorenz system satisfies the condition a12a21 > 0 while the Chen system satisfies a12a21 < 0. Very recently, Lü and Chen [2002] reported a new chaotic