具有扩展空间相互作用的时空混沌
Spatiotemporal Chaos with Extended Spatial Interactions
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中文总结 AI 辅助
本文利用协变李雅普诺夫向量（CLVs）研究扩展空间相互作用的一维非线性映射晶格的时空混沌，建立了仅依赖晶格耦合的理论方法，揭示CLVs的谱结构及两个区域的特性，确定了区域分界索引与动力学分形维数的关系。
中文摘要 AI 辅助
本文利用协变李雅普诺夫向量（CLVs）探究了空间耦合范围不断增大的大型一维非线性映射晶格的混沌动力学。研究建立了一种理论方法，可预测CLVs的谱变化及李雅普诺夫指数谱，该方法独立于映射函数的细节，仅需晶格耦合的描述。仅利用耦合矩阵的本征向量即可确定CLVs空间功率谱的一般结构，这将CLVs分解为两个区域：对应最大李雅普诺夫指数的第一区域包含高度纠缠的CLVs，其受大尺度空间结构的显著贡献，且与成对出现的排序本征向量对齐，这些本征向量的波数随索引线性增加；第二区域则随索引增大呈现长度尺度的显著混合，分隔两个区域的索引近似等于动力学的分形维数。
英文摘要
The chaotic dynamics of a large one-dimensional lattice of nonlinear maps with a spatial coupling of increasing extent is explored using the covariant Lyapunov vectors (CLVs). A theoretical approach is developed that predicts the spectral variation of the CLVs and the spectrum of Lyapunov exponents. The theoretical approach is independent of the details of the mapping function and requires only a description of the lattice coupling. The general structure of the spatial power spectrum of the CLVs is determined using only the eigenvectors of the coupling matrix. This yields a decomposition of the CLVs into two regimes. The first regime, corresponding to the largest Lyapunov exponents, contains highly entangled CLVs with significant contributions from large scale spatial structures and aligns with the sorted eigenvectors, which occur in pairs with wavenumbers that increase linearly with their index. The second regime contains significant mixing of length scales with increasing index. The index separating these two regimes is approximately equal to the fractal dimension of the dynamics.
发表机构
- Mechanical Engineering Department, Virginia Tech（弗吉尼亚理工大学机械工程系）
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