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推导了分数阶线性振子系统响应的一阶稳态矩的频率不变性和相移特性,并通过理论分析得出,在随机共振机制下,分数阶线性振子对系统响应一阶稳态矩的幅值具有放大作用.构造Duffing混沌振子检测器,利用混沌系统对参数摄动的敏感性以及对噪声的免疫能力实现弱信号检测.数值模拟证实,该方法可以有效地从噪声背景中将微弱正弦信号检测出来,并且相对传统的混沌检测方法能显著降低信噪比检测门限.
The frequency invariance and phase shift characteristics of the first order steady state moments of the fractional order linear oscillator system are deduced. Theoretical analysis shows that under the stochastic resonance mechanism, the fractional order linear oscillator responds to the first steady state moments The value of which has magnifying effect.We construct the Duffing chaotic oscillator detector and make use of the sensitivity of the chaotic system to the parameter perturbation and the weak signal detection to the noise immunity.Numerical simulation shows that this method can effectively reduce the weak sinusoidal signal Detected, and relative to the traditional chaos detection method can significantly reduce the signal to noise ratio detection threshold.