非线性随机耦合系统平衡点动力学新特性及其在微弱信号处理中的应用

This project study ‘new dynamic characteristic of equilibrium point in nonlinear stochastic coupled-systems and its application in weak signal processing’, which belongs to the basic researches of mathematical cutting-edge application that are driven by actual needs. Study of nonlinear stochastic coupled dynamics has gradually become a hot topic in mathematics and mechanics in recent years, however, due to the inherent complexity arising from the nonlinearity and randomness in the coupling system, there are many problems in the nonlinear stochastic coupled-systems need to be solved.. This project systematically study new dynamic characteristic of equilibrium point in nonlinear stochastic coupled-systems from the perspectives of mathematics and mechanics: ‘sensitive to regular signal parameters’ and ‘insensitive to random noise’, and analyze the effect of different types of noises and signals to these two characteristics, which has important theoretical significance. Meanwhile, aim at the key issues that need to be addressed urgently in engineering applications, this project propose detection and estimation methods for weak signals, on the basis of these two new characteristics and the theory of aperiodic coupled-stochastic resonance, which lays a foundation for breaking through the limitations in engineering applications and also has important applied significance.

本项目研究“非线性随机耦合系统平衡点动力学新特性及其在微弱信号处理中的应用”，属于有重大实际需求驱动和广泛实际背景的数学前沿应用基础研究。非线性随机耦合动力学的研究，在近年来逐渐成为数学及力学的研究热点，然而，由于非线性性、随机性在系统的耦合作用下所产生的内在复杂性，致使非线性随机耦合系统存在许多亟待解决的问题。. 本项目从数学及力学角度，系统性研究非线性随机耦合系统平衡点吸引子所具有的“驱动参数敏感性”以及“随机噪声不敏感性”这两大动力学新特性，分析不同类型噪声和驱动对此特性的影响关系，具有重要的理论意义；另一方面，从工程技术应用特别是国防科技研究中迫切需要解决的关键问题出发，将非线性动力学引入微弱信号处理中，利用所研动力学新特性，结合非周期耦合随机共振原理实现微弱信号的检测及估计，为突破工程应用的局限奠定基础，也具有重要的应用前景。

本项目从数学及力学角度进行研究，所得结果涉及理论研究和应用研究两方面。在理论研究方面，系统性地研究了非线性及分数阶随机动力学系统定常和混沌吸引子所具有的动力学特性以及各类随机共振现象，在定常吸引子研究及应用、分数阶混沌构造和随机共振等领域均取得了新的结果；在应用研究方面，基于理论研究的成果，将非线性动力学引入微弱信号处理中，利用所研动力学新特性实现了弱信号参数估计和分数阶系统参数辨识，同时也针对分数阶参数估计理论在雷达信号处理的应用提出了新的方法技术；从工程技术应用特别是国防科技研究中迫切需要解决的关键问题出发，将所得成果应用于雷达等相关领域的国防军工项目中，取得了显著的效果。