Duffing系统的欧拉实现方法研究

Implementation of duffing system based on Euler equations

在研究Duffing系统的基础上,为了利用Duffing系统进行弱信号检测,必须实现一种可靠的Duffing系统模型。对3种基于欧拉方程的模型实现方式进行了对比,通过分析欧拉方程的几何意义,并结合DSP Builder的特点,提出了一种易于工程实现的改进欧拉形式。通过对四种算法进行仿真实验得出,运用不同的状态模型建立Duffing系统会改变振子相变的临界策动力幅值,但不会对系统固有存在的状态产生影响。

In order to use the Dulling system to detect weak signal, a reliable Dulling system model must be achieved. Three realization modes of model based on Euler equations are compared. By analyzing the geometric meaning of the Euler equations and combining the characteristics of DSP Builder, an improved Euler form which is easy to realize in engineering is proposed on the basis of the related research on Dulling system. The simulation experiments for four algorithms indicate that the establishment of Buffing system with different state models can change the critical driving force amplitude of the oscillator phase transition, but can not affect the inherent status of the system.