  The dynamics of unidirectionally coupled chaotic Lorenz systems is
investigated. It is revealed that chaos is present in the response system
regardless of generalized synchronization. The presence of sensitivity is
theoretically proved, and the auxiliary system approach and conditional
Lyapunov exponents are utilized to demonstrate the absence of synchronization.
Periodic motions embedded in the chaotic attractor of the response system is
demonstrated by taking advantage of a period-doubling cascade of the drive. The
obtained results may shed light on the global unpredictability of the weather
dynamics and can be useful for investigations concerning coupled Lorenz lasers.
