Connecting the Lorenz and Chen systems via nonlinear control

The Lü system is a new chaotic system, which connects the Lorenz system and the Chen system and represents the transition from one to the other. In this letter, based on the concept of nonresonant parametric perturbations, further detailed analysis about the forming mechanism and its compound structure for the chaotic Lü system are offered. The obtained results clearly reveal the intermediate chaotic system has another novel forming mechanism: the compression and pull forming mechanism, which provides an enlighten insight about the relationship of its vibration “mode” and the two-scroll “base” chaotic attractor. Then motivated by this novel forming mechanism, by adding a simple nonlinear term to the Lü system, 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.