Chaotic Diffusion in Delay Systems

延迟系统中的混沌扩散

• 批准号: 438881351
• 负责人: Professor Dr. Günter Radons
• 金额: --
• 依托单位: Forschungsgruppe Komplexe Systeme und Nichtlineare Dynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/438881351?language=en
• 关键词: Chaotic; Diffusion; Delay; Systems

Chaotic diffusion is a well-known deterministic phenomenon in nonlinear dynamical systems, where the state variable shows normal or anomalous diffusive motion. A thorough understanding of the mechanisms leading to normal or anomalous diffusion was achieved mainly for low-dimensional dynamical systems. Recently renewed interest was triggered by questions of ergodicity breaking in such systems. Delay systems, on the other hand, are very general and practically relevant systems, where finite transmission times of reactions are explicitly taken into account. These formally infinite-dimensional systems have a long history, but surprisingly, the appearance of diffusive motion in such systems has hardly been investigated. Our recent detection of laminar chaos, a new form of chaotic motion in delay systems, provides also hitherto unknown mechanisms for normal and anomalous diffusion in delay systems, thus connecting two traditional branches of nonlinear dynamics. The general goal of this project is to explore the properties of diffusive motion in such delay systems, including questions of ergodicity breaking, and the scenarios appearing in the transition from laminar to turbulent chaos.

混沌扩散是非线性动力系统中众所周知的确定性现象，其中状态变量显示正常或异常扩散运动。主要针对低维动力系统，对导致正常或异常扩散的机制有了透彻的了解。最近，此类系统的遍历性破坏问题再次引发了人们的兴趣。另一方面，延迟系统是非常通用且与实际相关的系统，其中明确考虑了反应的有限传输时间。这些形式上的无限维系统有着悠久的历史，但令人惊讶的是，此类系统中扩散运动的出现几乎没有被研究过。我们最近对层流混沌（延迟系统中混沌运动的一种新形式）的检测，还为延迟系统中的正常和异常扩散提供了迄今为止未知的机制，从而连接了非线性动力学的两个传统分支。该项目的总体目标是探索此类延迟系统中扩散运动的特性，包括遍历性破坏的问题以及从层流混沌过渡到湍流混沌时出现的场景。