Anticontrol of chaos via direct time delay feedback

Purposely generating chaos when useful becomes an increasing focus of chaos research. Direct time delay feedback is proposed for anticontrol of chaos, which generates chaos from non-chaotic systems. Compared with the indirect time delay feedback, direct time delay feedback control is simple and easy to realize. The proposed method has the same structure as the time delay feedback method proposed by Pyragas for chaos control, therefore, the proposed method can generate chaos when it is useful, and eliminate chaos, when it is harmful, which will provide the designer with maximum flexibility. Simulations with nonchaotic Chen system and Lorenz system show the effectiveness of the proposed method.