  We demonstrate the extension of unpredictable motions in coupled autonomous
systems with skew product structure in the case that generalized
synchronization takes place. Sufficient conditions for the existence of
unpredictable motions in the dynamics of the response system are provided. The
theoretical results are exemplified for coupled autonomous systems in which the
drive is a hybrid dynamical system and the response is a Lorenz system. The
auxiliary system approach and conditional Lyapunov exponents are utilized to
detect the presence of generalized synchronization.
