Abstract
The purpose of this investigation is the applications of the feedback control method in order to control the behavior of the new hyperchaotic system. We consider hyperchaotic system first and then apply the feedback control method to obtain the results for the control of the hyperchaotic system. We present some conditions on the parameters values and show that the controlled system is stable which is established by the Routh–Hurwitz criterion. We also show results for the adaptive modified function projective synchronization (AMFPS) of two identical new hyperchaotic systems with known parameters. Using the Lyapunov stability theory, we can present the system that the is asymptotically stable. At last, we provide numerical results for the justifications of the theoretical results by considering the initial values of the variables and the suitable parameters values. The simulated results justify the importance of the considered method.