分数阶Duffing系统动态特性研究及微弱信号检测

为了进一步提高微弱信号的检测能力，在更低信噪比环境下提取微弱信号的特征信息，提出采用分数阶Duffing系统实现微弱周期信号检测。基于常规Duffing-Holmes数学模型 ，通过加入分数阶微分算子引入了分数阶Duffing方程数学模型，利用变量代换对该模型进行改进可实现任意频率的微弱周期信号检测。研究分析系统阻尼比参数变化对系统非线性动力学特性的影响，给出了最佳阻尼比参数范围；研究了微分阶次与系统临界混沌阈值变化关系，得出微分阶次与系统临界混沌阈值成反比关系的结论。分别在高斯白噪声及色噪声背景下对微弱信号进行检测与识别，大量仿真结果表明，分数阶Duffing系统检测微弱信号的最低信噪比门限值比整数阶Duffing系统降低了10 dB，提高了检测微弱信号能力。

Dynamic characteristic research and weak signal detection of fractional order Duffing system

In order to improve the detection ability and extract the characteristic information of weak signal in lower signal noise ratio(SNR) environment, the detection of weak periodic signal using fractional order Duffing system is proposed. Based on conventional Duffing-Holmes mathematical model, the mathematical model of fractional order Duffing equation is introduced by adding the fractional differential operator, and it can detect the weak periodic signal of arbitrary frequency by using variable substitution for the model. The optimal damping ratio parameters are given by studying the system damping ratio parameters effect on the nonlinear dynamics characteristics, and the inverse relationship is obtained by studying the differential order and the critical chaos threshold change. To detect and identify the weak signal in the Gauss white noise and colored noise background, a large number of simulation results show that the minimum SNR threshold value of weak signal detection with fractional order Duffing system which improves the ability of detecting weak signals is 10 dB lower than the integer order Duffing system.