Duffing振子临界态性能研究

Research on the Performance of the Duffing Oscillator Critical States

During振子临界态相变对弱信号检测研究非常重要，文中研究During临界状态的性能。介绍了随机微分方程理论关于噪声对系统周期态影响的分析；然后为克服存在的过渡过程，建立改进的系统仿真模型。通过仿真试验分析During振子临界态的性能，混沌态与大尺度周期态表现的性能差别深化了对混沌现象的认识；重点研究受噪声干扰的系统运动状态变化情况，得出系统运动越接近临界态越对噪声敏感，噪声越强周期态运动容易再次跃迁回混沌态，说明随机微分方程理论分析临界状态结果不正确；实验结果还表明，噪声是在某些特定条件下导致处于临界大尺度周期态运动的系统发生突变分又跃迁回混沌状态，值得进一步深入研究。

The Duffing system phase change between its critical states is very important for weak signal detection. The performance of the critical states was researched in this paper. Firstly the stochastic differential equation theory was introduced to analyze the noise affection on the large scale period states, then the improved Duffing system simulation model was build up which got over the transition process. The performance of critical states was studied by simulating. The chaos state and period state show very different capability, from which we can understand the chaos phenomenal more deeply. The system state change under the noise interfering was analyzed specially, the state close to the critical state is very sensitivity to the noise, and the stronger noise the more period state transit to chaos states, which is not agree with the result of stochastic differential equation theory. The experiment also illustrated that the noise induced the period movement state into chaos state through break and bifurcation, which was happened in some more especial condition, that all deserved more deeply study in theory.