Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system

Ultimate bound sets of chaotic systems have important applications in chaos control and chaos synchronization. Ultimate bound sets can also be applied in estimating the dimensions of chaotic attractors. However, it is often a difficult work to obtain the bounds of high-order chaotic systems due to complex algebraic structure of high-order chaotic systems. In this paper, a new 5D autonomous quadratic chaotic system which is different from the Lorenz chaotic system is proposed and analyzed. Ultimate bound sets and globally exponential attractive sets of this system are studied by introducing the Lyapunov-like functions. To validate the ultimate bound estimation, numerical simulations are also investigated.