A novel method to identify the scaling region for chaotic time series correlation dimension calculation

To obtain more accurate correlation dimension estimations for chaotic time series, a novel scaling region identification method is developed. First, points that obviously do not belong to the scaling region associated with the whole double logarithm correlation integral curve are removed using the K-means algorithm. Second, a point-slope-error algorithm is developed to recognize a possible scaling region. Third, the K-means algorithm is used again to further remove a small interval of interfering points in the possible scaling region to obtain a more precise scaling region. The correlation dimension of four typical chaotic attractors and five curves generated by the Weierstrass-Mandelbrot fractal function were calculated using the proposed method. These calculated values were very close to the respective theoretical fractal dimensions. Moreover, the effectiveness of our method in identifying the scaling region was compared with existing methods. Results show that our method can distinguish the scaling region objectively, accurately, automatically and quickly, making estimations of the correlation dimension more precise and affording significant improvements in nonlinear analysis.     

霍金温度的修正对半全息宇宙学模型的影响

文章修正了霍金温度的一般形式,基于其表达式中标度因子a的二阶导数项的动力学效应,重新讨论了半全息宇宙学模型下暗能量和暗物质比例的巧合性问题与宇宙加速问题,得到了宇宙动力学方程及其吸引子解,并给出了宇宙减速因子和等效压强密度比的解析表达式.在给定合理的参数后,宇宙减速因子取负值,表明当前的宇宙正在加速膨胀,同时暗能量和暗物质的等效压强密度比也符合半全息宇宙学的预期结果.     

一类高阶有理差分方程的全局渐近稳定性

研究差分方程xn+1=xn+αxn-k/Axn+Bxn-k,n=0,1,2,…,所有正解的局部稳定性、素二周期解、有界性、不变区间和全局渐近稳定性,其中α,A,B∈(0,∞),k∈{1,2,3,…},初始条件x-k,…,x0是任意的正整数.获得了此方程的唯一正平衡点是全局渐近稳定的.     

某类柯西变换的罗朗系数性质

假设{Sj}q-1j=0是由压缩映射Sj(z)=εj ρ(z-εj)(1.1)组成的迭代函数系(IFS),其中0<ρ<ρq,εj=e2jπiq(ρq的定义见[1]),K是{sj}q-1j=0的吸引子,μ是支撑在K上的Hausdorff测度,最近,文[1]中讨论了自相似测度的柯西变换F(z)=∫K(z-w)-1dμ(w)在|z|>1内的罗朗系数.本文主要研究H(z)=∫K(λz-w)-1dμ(w)在|z|>1内的罗朗系数,其中|z|=1.得到了一些结果.     

Learning,Mutation and the Economics of Convention:A Selected Review of Evolutionary Game Theory

Before the present of basic model,one example is given in section 2 to illustrate the economic intuition behind the SSE. The general model,including the three hypotheses,adaptive play setting and basic results is laid out in section 3. Sections 4 study the asymptotic behavior of this model. This review concludes with a comment.     

高炉炉况的动态辨识

用ＧＰ算法以及修正ＧＰ算法对高炉风量、料柱压差、鼓风压力等高炉过程变量时间序列的相关维数进行了移动估算和预报能力分析。结果表明：在研究范围内不能发现高炉炉况吸引子存在；而预报能力的变化与高炉炉况变化前兆之间存在明显对应关系，可用于炉况辨识。     

坍塌孤立波方程的吸引子与分形维估计

本文研究坍塌孤立波方程的无穷维动力系统长期特征,研究它的时间混沌与吸引子的分形维估计。     

混沌吸引子分维数的极限分辨率自归算法

根据混沌吸引子的数值特性与数据采集器的分辩率有限的特性,提出的快速算法,实现了在AT系列微型计算机上以实时或近乎实时的计算速度,从实验数据中,计算出混沌吸引子的分维数。     

关于Cauchy中值定理“中值点”的一个一般性结果

讨论了Cauchy中值定理"中值点"当区间长度趋于零时的渐近性质,得到了一个具有一般性的新结果.     

一类广义kdv的整体吸引子

通过对广义kdv方程的初值问题的整体解关于时间t作一致估计,得到了解的整体吸收集,从而证明了其整体吸引子的存在性.