In this paper we study the impact of tiny mutation on the evolutionary dynamics on one-dimensional cycle with shifting mechanism. The evolutionary success is evaluated by investigating the stationary distribution of the ergodic process with the idea of viscosity solutions. The cooperative behaviors in ecosystem and social system are briefly discussed by applying the results to the prisoner's dilemma game.

非平稳性是水资源系统复杂性的一个重要方面,也是业界关注的理论难点之一.以稳定集合的概念为出发点,基于概率论中的中心极限定理及大数定律,探讨了可用于水文时间序列处理的稳定集合判别准则,并在仿真实验的基础上给出了选参经验公式以减小参数选择的主观性.在稳定信息结构的基础上给出了时间序列的非平稳度量指标并将其应用到模型选择问题中.借鉴AIC信息准则等方法,非平稳度量指标的提出为模型选择问题提供了一种新的准则:残差序列非平稳性度量最小化方法.利用该方法探讨农业灌溉用水量预测模型的优选问题,以长江支流举水流域的灌溉用水量预测为实例进行说明,并讨论了方法的有效性.

Flood forecasting errors and net rainfall forecasting errors are important risk source for current forecast dispatching of reservoirs,and affect fulfilling the integrated benefit of reservoir fully.Taking the flood forecasting errors and net rainfall forecasting errors as the loads of forecasting system for reservoirs,the reliability of flood forecasting system is analyzed based on the reliability theory,the reliability indices of single failure mode of net rainfall forecasting and flood forecasting of Dahuofang reservoir are obtained based on Monte Carlo simple method at first;then the impact of different types of performance function on the system reliability index of flood forecasting is analyzed;and the system reliability index of flood forecasting is presented in the determinative performance function condition based on the adaptive methods of importance sampling method,including adaptive first order reliability method and adaptive second order reliability method.The results obtained in this paper could give theoretical basis for improving the level of flood forecasting.