New results on connecting the Lorenz and Chen Systems

The Lü system is a newly coined chaotic system, which connects the Lorenz system and the Chen system and represents the transition from one to the other. In this letter, a simple nonlinear term is added to the Lü system, and its role as a joint function is revisited. With the gradual tuning the parameter of the nonlinear controller, the transition from the canonical Lorenz attractor to the Chen attractor through the Lü attractor is revived. The scheme herein goes beyond the traditional framework for studying the Lorenz-like systems, which can be very helpful in generating and analyzing of all similar and closely related chaotic systems.