Boundedness solutions of the complex Lorenz chaotic system

This paper is concerned with the boundedness of solutions of the complex Lorenz system. We have obtained the global exponential attractive set Ψλ,mΨλ,m and the ultimate bound Ωλ,mΩλ,m for this system. Furthermore, we confirm that the rate of the trajectories of the system going from the exterior of the set Ψλ,mΨλ,m to the interior of the set Ψλ,mΨλ,m is an exponential rate. The rate of the trajectories is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.