A common phenomenon in chaotic systems linked by time delay

作者：Yu Pei^*; Xu Fei

来源：International Journal of Bifurcation and Chaos, 2006, 16(12): 3727-3736.

DOI：10.1142/S0218127406017129

• Lorenz system
• Rossler system
• Chen system
• Chua's circuit
• 4-Liu system
• time delay

In this paper, we report a common phenomenon observed in chaotic systems linked by time delay. Recently, the Lorenz chaotic system has been extended to the family of Lorenz systems which includes the Chen and Lu systems. These three chaotic systems, corresponding to different sets of system parameter values, are topologically different. With the aid of numerical simulations, we have surprisingly found that a simple time delay, directly applied to one or more state variables, transforms the Lorenz system to the generalized Chen system or the generalized Lu system without any parameter changes. The existence of this phenomenon has also been found in other known chaotic systems: the Rossler system, the Chua's circuit and the 4-Liu system. This finding has shown a common characteristic of chaotic systems: a new chaotic "branch" can be created from a chaotic attractor by simply adding a time delay.

• 出版日期2006-12