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

Based on the Lü chaotic system, a new four-dimensional hyperchaotic Lü system with higher order nonlinear term is constructed, and the basic dynamic behaviors of the system are studied. 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 Lü system is controlled to equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.