有界噪声激励下Hénon-Heiles系统响应的降噪分析

针对有界噪声激励下Hénon-Heiles系统响应的杂乱特性,通过改进一类降噪算法,给出经降噪算法处理后响应的重构特征及相应最大Lyapunov指数.结果表明：经改进后的算法在处理Hénon映射的含测量噪声的混沌吸引子时更为有效；有界噪声激励使Hénon-Heiles系统的样本响应远离无噪声时的确定轨迹,但经过改进的降噪算法处理后的重构相图能体现出确定情形下系统的固有特性；可利用这一改进算法对杂乱输出信号进行混沌特征提取与分析；在系统无法避免噪声激励干扰的情况下,主动地适度增加随机激励的强度可能会得到更好的混沌特性识别效果.

Noise reduction on sample responses of Hénon-Heiles system subjected to bounded noise excitation

A customary algorithm on noise reduction has been developed to explore the characteristics of the reconstructed orbits and their corresponding largest Lyapunov exponents in the Hénon-Heiles system. It is shown that the developed algorithm is more effective to deal with the chaotic attractor with measurement noise in the Hénon map, and the reconstructed phase portraits can open out the intrinsic dynamics in the original deterministic Hénon-Heiles system by the developed algorithm, though the sample responses may escape far away from the noiseless orbits. Hence, the developed algorithm can be applied to extract the features of chaotic orbits from the irregular output signals. Moreover, when dynamical noise is inevitable, moderately increasing the strength of the dynamical noise is recommendable to identify the irregular signals in some cases.