分数阶随机共振行为机制及其自适应控制与强色噪声背景中的微弱信号检测

The project study on the behavior mechanism and adaptive control of the stochastic resonance of fractional stochastic dynamical systems, and its application in the weak signal detection under strong colored noise background.. In recent years, fractional stochastic dynamics is derived from the study of many complex phenomena, such as anomalous diffusion and transport process. As the system's typical nonlinear phenomenon, stochastic resonance has received great attention. However, until now the creation conditions, behavior mechanism and action mode of the stochastic resonance of fractional stochastic dynamical systems is not clear yet. The serious lack of strict mathematical theory of support also constrained its application. On the other hand, fractional stochastic resonance has the outstanding advantages that translating noise energy into signal energy, which is broadly required in engineering applications. How to introduce it into weak signal processing, and then break the detection limit of the traditional method, is the important issue which need to be addressed urgently in signal detection field.. For the inherent complexity arising from fractional derivative, this project will start the related work by the way of fractional analysis. The to-be studied content of the project is significant in both the theoretical research and the engineering applications including national defense high technology, which belongs to the mathematical frontier theory driven by great practical needs.

本项目研究分数阶随机动力系统的随机共振行为机制及其自适应控制，并将其应用于强色噪声背景下的微弱信号检测问题。. 近年来，对反常扩散、输运过程等诸多复杂现象的研究衍生出了“分数阶随机动力学”，随机共振作为系统的典型非线性现象，受到了广泛关注。然而，分数阶随机动力系统的随机共振产生条件、行为机制、作用方式等问题至今未能厘清，更缺乏严格数学理论支撑，使其应用备受限制。另一方面，分数阶随机共振"将噪声能量转化为信号能量”的突出优势，使其在工程技术应用特别是微弱信号检测中受到迫切需求，如何将其引入微弱信号处理中，突破传统方法检测极限，是信号检测领域亟待解决的重要问题。. 针对分数阶微分带来的系统内在复杂性，本项目拟从分数阶分析学角度展开相关研究工作。项目拟研究内容在理论科学研究和工程技术应用特别是国防高科技研究中均具重要意义，属于有重大需求驱动的数学前沿应用基础研究。

本项目研究“分数阶随机共振行为机制及其自适应控制与强色噪声背景中的微弱信号检测”，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。分数阶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，由于分数阶、随机在系统的耦合作用下所产生的内在复杂性，致使分数阶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，系统性研究分数阶随机耦合系统中的重要前沿问题，具体包括：分数阶随机动力系统的共振行为机制及其共振、随机共振的自适应控制，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，将分数阶随机共振理论引入微弱信号处理中，利用所研共振行为机制及自适应控制方法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。

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