Impacts of Random Error on the Predictability of Chaotic Systems
随机误差对混沌系统可预报性的影响

Based on the nonlinear local Lyapunov exponent (NLLE) approach, the influences of random error and initial error on the predictability of the Logistic map and the Lorenz system are studied. The influences of initial error and random error on the predictability mainly depend on their relative magnitudes. When the magnitude of initial error is much greater than that of random error, the predictability limit of two systems is mainly determined by the initial error. On the contrary, when the magnitude of random error is much greater than that of initial error, the predictability limit of two systems is mainly determined by the random error. When the magnitude of initial error is close to that of random error, both of them contribute to the predictability limit of two systems. In addition, the authors have investigated the influences of random error on the predictability by integrating the error growth equations. The results are similar to those obtained using experimental data. This finding indicates that due to the impacts of random error, only an approximation of the true predictability of chaotic systems can be obtained when the random error is sufficiently small. It is impossible to obtain the true predictability for large random errors. The present study also attempts to use the filtering method to reduce the impact of random error on the estimates of the predictability limit of chaotic systems. The results show that by using the high-pass Lanczos filter, both the high-frequency sequence and the noise sequence perform conformably either in intensity or in the evolution of trends. This method can effectively remove the random noise and then improve the estimate of the predictability limit of chaotic systems, which also gives some enlightenment to the removal of the noise contained in observational data.