周期势系统中噪声诱导共振现象的研究

项目名称： 周期势系统中噪声诱导共振现象的研究

项目编号： No.11272051

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 靳艳飞

作者单位： 北京理工大学

项目金额： 78万元

中文摘要： 研究非线性随机动力系统中由噪声诱导的共振现象，揭示其产生的条件、机理，是随机动力学领域关注的热点问题，具有较强的应用背景。 本项目以周期势系统为研究对象，拟开展以下研究工作：研究不同类型噪声激励下，周期势系统的随机共振、自随机共振和共振激活现象，包括高斯色噪声和三态马尔科夫噪声激励的情形；研究加性和乘性高斯白噪声共同作用下含时滞周期势系统的随机共振、自随机共振和共振激活，分析噪声和时滞对共振行为的影响，揭示共振产生的条件和机理；作为应用，研究高斯噪声激励下约瑟夫森结中的随机共振、自随机共振及共振激活现象，包括无时滞系统和含时滞系统两种情况，其研究结果能为超导器件的实验研究提供一定的理论基础；通过搭建动力学实验平台对含时滞约瑟夫森结系统进行随机共振和共振激活的实验研究，验证理论结果的有效性。

中文关键词： 周期势系统；随机共振；自随机共振；噪声；时滞

英文摘要： Noise-induced dynamical behaviors,such as stochastic resonance (SR), coherence resonance (CR) and resonant activation (RA), have been attracted great attention of people from many fields. Studying the condition and the mechanism of noise-induced resonances is of great significance for its widely potential applications. This project mainly studies SR, CR and RA in the periodic potential system driven by different type of noises. The study contents include: Noise-induced resonances are studied in the periodic potential system driven by colored Gaussian noise or three-state Markovian noise;The resonance behaviors are studied in the delayed periodic potential system subject to additive and multiplicative Gaussian white noises. The effects of noises and time delay on the resonance behaviors are presented. Meanwhile, the condition and mechanism of resonances are explored to explain the complex nonlinear phenomena; As an application, the resonance behaviors are investigated in the Josephson Junction driven by Guassian noises. The study results will provide a theoretical basis for the experiments of superconducting device; SR and RA are investigated by dynamical experiments of the periodic potential system. The theoretical results are verified by the experimental results.

英文关键词： Periodic potential system；stochastic resonance；coherence resonance；noise；time delay