混沌系统可预测尺度研究

Study on the Predictable Size of Chaotic Systems

着重讨论了混沌系统未来状态预测的 "长期 "与 "短期 "问题 .混沌系统的初始状态敏感性决定了其不可长期预测性 .但在短期内对混沌系统的运动作出准确预测还是可能的 .基于此 ,给出了混沌时间序列的平均可预测尺度及最长可预测尺度 ,以此来界定短期预测的时间范围 .最后利用 Logistic映射以及 Henon映射产生的混沌时间序列对上述理论进行了实例验证 ,得到了较为理想的结果 .

This paper focuses on the problem of long-term and short-term future states prediction of chaotic system. Sensitiveness of chaotic system to the original state determines that it is impossible to predict its future states in long term. However, it is realistic to make proper prediction on the movement of chaotic system in short term. Based on this, the average predictable size and the longest predictable size of chaotic time series are provided in this paper to definite the time range of short-term prediction. In the end, two kinds of chaotic time series generated by Logistic map and Henon map are utilized to verify the theory above.