最大Lyapunov特性指数在微弱信号检测中的应用

Application of maximal Lyapunov exponent to weak signal detection

利用Duffing振子的运动状态来判断微弱信号的存在是一种常用的方法,通常此方法没有明确的门限。由于最大Lyapunov特性指数是指示动力学系统是否处于混沌状态的重要参数,所以将最大Lyapunov特性指数作为混沌判据引入基于Duffing振子的微弱信号检测中。利用最大Lyapunov特性指数指示Duffing振子所处的状态,如果最大Lyapunov特性指数大于1,测说明系统处于混沌状态,反之则处于周期状态,从而为此方法提供了更为直观的判断依据。仿真结果表明,采用最大Lyapunov指数作为判断依据可以更准确的判断微弱信号的存在,进而说明此方法的可行性。

Duffing systems are commonly used in weak signal detection. Unfortunately, this method does not have any specific threshold. The maximal Lyapunov exponent （LE） is introduced in Duffing systems since it is an important parameter denoting whether the dynamics system is chaotic. If the maximal LE of the system is positive, it is chaotic. Otherwise it is periodic. This provides an easy decision criterion. Simulation results indicate it is more accurate than other methods.