A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter $k$. Furthermore，effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.