Narrow Results

The disappearance and reappearance of chaos by adjusting the internal parameters of dynamics in Lorenz system are studied. We observe monotonous and periodic time-dependent changes of Rayleigh number. There exists relaxation time for the disappearance of chaos, when we use the snapshot attractors to observe the change of the system attractors. We show that the rate of disappearance and reappearance of chaos is positively correlated with the control parameters. To reflect the relaxation phenomenon of chaotic disappearance and the sensitivity of trajectory, the concept of finite-time Lyapunov exponent is used. Then the statistical characteristics of the system can be presented by standard deviation. The chaotic disappearance and reappearance are manifested in the decrease and increase of the standard deviation. The standard deviation decreases continuously during chaotic disappearance, but increases discontinuously during chaotic reappearance. A distinctive scenario is that no matter which parameter changes, when we use the same rate of change in the process of chaotic disappearance and reappearance, their paths are different.