A study on chaotic systems with time delay

Since the discovery of the Lorenz chaotic attractor, great progress has been achieved in the study of chaotic systems. Recently, the Lorenz system has been extended to the family of Lorenz systems which includes the Chen system and the Lu system. The Lorenz system, the Chen system and the Lu system, corresponding to different set of system parameter values, are topologically different. In this paper, with the aid of numerical simulations, based on the Lorenz system with fixed parameter values, we apply time delay into one or more state variables and surprisingly find that this approach can recover the Chen system and the Lu system without parameter changes. This method is also applied to consider the Wissler system and the Chua's circuit, and similar results are obtained.