Generating a hyper-chaotic system from 3D chaotic behaivor

In the past studies, researchers have always produced new hyper-chaotic systems without explaining how to add the fourth equation in the 3D system. In this paper, we are interested in searching a link between the 3D and 4D system through which it designs a hyper-chaotic system 4D. We have constructed new hyper-chaotic systems by adding another state variable in the chaotic dynamical systems to the three dimensions which were developed by Lorenz [1], Lü [2] and Rossler [3]. The development of the proposed systems is achieved through a combination of computer simulation via Matlab and mathematical analysis to find the hyper-chaotic attractors and the Lyapunov exponents.