【摘要】 以Logistic映像为例,运用非线性动力学的方法,分析了不同信噪比时,噪声对离散映像在混沌区非线性特征量的影响.通过错误近邻分析法确定序列的嵌入维,计算了序列的关联维数、最大Lyapunov指数和近似熵,结果表明:随着信噪比的降低,关联维数和近似熵逐渐增大,最大Lyapunov指数呈下降趋势;当信噪比大于500时,噪声对非线性特征量的影响不大.并采用重现图形和重现定量分析法得出信噪比大于10时序列存在的确定性规律仍能显示出来.更多还原

【Abstract】 This paper,uses several nonlinear means to analyze the effects of noise to the nonlinear values of chaotic discrete system.It uses Logistic map as an example.At first,uses the method of false nearest neighbors analysis to determine the embedding dimension. It calculates the correlation dimension(Dc),the largest Lyapunov exponent (λ1)and the approximate entropy .It shows that the correlation dimension and approximate entropy increase and the largest Lyapunov exponent decreases with the drop of PSNR.The influence of noise is not obvious when the PSNR is not less than 500.It uses the method of recurrence plot analysis(RPA)and recurrence quantification analysis(RQA)to get the conclusion that all the series obey the deterministic rule when the signal-to-noise ratio(PSNR)is greater than 10.更多还原