The bound for a class of four-dimensional hyperchaotic system and its synchronization

In this paper, a class of four-dimensional continuous autonomous system is studied. It has only one balance under certain conditions but it shows a complicated dynamic behavior. The equilibrium points and lyapunov exponents of the system are analyzed. The bound of this system is estimated and the expression of the bound is presented. In addition, the complete synchronization is also discussed by designing a linear controller. Finally, the corresponding numerical simulations are performed.