[author_cn_name].[cn_title][J].空军工程大学学报:自然科学版,[year_id],[volume]([issue]):[start_page]-[end_page] 基于庞加莱截面点的二阶混沌系统状态的定量判别-The State Quantificational Judgment on Second Order Chaos Based on the Poincare Section Points
文章摘要
蔺向阳,陈长兴,凌云飞,黄继尧.基于庞加莱截面点的二阶混沌系统状态的定量判别[J].空军工程大学学报:自然科学版,2019,20(2):86-93
基于庞加莱截面点的二阶混沌系统状态的定量判别
The State Quantificational Judgment on Second Order Chaos Based on the Poincare Section Points
  
DOI:10.3969/j.issn.1009-3516.2019.02.013
中文关键词: 混沌状态  Duffing振子  庞加莱截面点  离差均方值
英文关键词: chaotic state  Duffing oscillator  Poincare section points  deviation's mean square value
基金项目:国家自然科学基金(61701534)
作者单位
蔺向阳,陈长兴,凌云飞,黄继尧 空军工程大学研究生院,西安,710051 
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中文摘要:
      为增强对二阶混沌系统状态判别的效率与准确性,基于Duffing振子特性,利用庞加莱截面点密集程度作为其系统混沌状态的判据,构造相应函数模型用以定量表征其系统状态判据。利用特定参数下二阶混沌系统表现出的不同程度的周期特性,以策动力周期为采样周期对系统输出进行等周期频闪采样,获得庞加莱截面点。通过对固定数目的相邻样点离差均方值进行计算,定量表征出其样点分布的集中程度。通过进一步实验确定合适的阈值,实现混沌状态的判别。基于混沌的基本特征,实现从系统庞加莱截面点的角度进行混沌状态的判断,减小了运算复杂度,弱化了计算机数值解的计算误差的影响,增加检测准确度。通过选择合适系统初值与采样区间,缩短了采样时长,进而缩短判定时间,提高判定效率。后以二阶周期驱动的Duffing振子为例进行实验,得到实验结果,证明了此定量判别方法的可行性。通过复现前人实验并与本实验结果进行对比,突出本判定方法相比于前人,具有更高的准确度与更快的判定效率。
英文摘要:
      In order to judge the state of second order chaos system more accurately and efficiently, in this paper, starting from the characteristic of Duffing oscillator and using the intensity of Poincare section points as the criterion of chaotic state, a quantitative description has been developed to distinct the state of chaotic by constructing a function. The method is mainly according to different periodic characteristic of second-order chaotic system showing in specific conditions. To obtain the Poincare section points, the system output is sampled as a constant period, which is all just the same to the period of the driving force. Based on the calculation to the deviation's mean square value of a fixed number of adjacent sampling points, this method indicates concentrate degree of the sampling points' distribution quantificationally. Then through the further experiment, an appropriate threshold can be determined and the chaotic state can be judged. The method directly uses the basic characteristics of chaos as the criterion to realize the chaotic state judgment from the system Poincare section's point, greatly reducing the computation complexity, weakening the effect of the machine error when computer numerically is calculating and the detection accuracy is increasing. The result shows that the sampling time is shortened, thus shortening the time of decision and improving the efficiency of decision. Through conducting an experiment by using the Duffing oscillator driven by Second order periodic force as an example, an anticipative conclusion is reached to prove the feasibility of the theory. By reproducing the experiments of former theory, and compared this theory to the former, this theory has higher accuracy and efficiency.
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