Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

For Chen-Qi-like four-dimensional hyper-chaotic system, controllers designed with Lyapunov stability theory to achieve synchronous/anti- synchronous control of chaos are found that sometimes synchronization errors do not decrease to zero in finite time. To solve it, a new controller and parameter estimation law are proposed to achieve finite-time synchronization. The stability analysis of the closed-loop dynamics is derived and the effectiveness of the theoretical results is testified. Taking the parameters L=2, μ=0.5, the state time history diagram and the synchronous error curve are investigated via numerical simulation, which show that the synchronization errors are zero in finite time while two systems in chaotic motion, but synchronization error of the state with cubic nonlinearity is not zero in finite time while two systems in periodic motion; Adjust L=200,μ=0.5, numerical simulation again, then all the errors are zero in finite time. Thus the effectiveness is verified.