[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
The State Quantificational Judgment on Second Order Chaos Based on the Poincare Section Points
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
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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      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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