A new four-dimensional hyperchaotic Lorenz system and its adaptive control

Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh–Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on Lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.