保证扩散耦合系统中的空间均匀性
Guaranteeing Spatial Uniformity in Diffusively-Coupled Systems
AI总结：
本文提出一种基于雅可比矩阵和图拉普拉斯特征值的条件，用于保证扩散耦合隔室ODE模型以及具有Neumann边界条件的反应扩散PDE解的空间均匀性，并允许各组分具有独立的扩散项和互连结构。
摘要：
我们提出了一个条件，该条件保证扩散耦合隔室ODE模型的解轨迹的空间均匀性，其中每个隔室代表一个空间域，其组分通过扩散项与不同隔室中的同类组分相互连接。每组同类组分都有自己的加权无向图，描述隔室间互连的拓扑结构。该条件利用雅可比矩阵描述每个隔室的动力学以及每个图的拉普拉斯特征值。我们讨论了可用于验证保证空间均匀性条件的线性矩阵不等式，并将结果应用于耦合振荡器网络。接下来，我们转向具有Neumann边界条件的反应扩散PDE，并推导出保证解的空间均匀性的类似条件。本文贡献了一个放宽的条件来检查空间均匀性，允许单个组分具有其特定的扩散项和互连结构。
英文摘要：
We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components has its own weighted undirected graph describing the topology of the interconnection between compartments. The condition makes use of the Jacobian matrix to describe the dynamics of each compartment as well as the Laplacian eigenvalues of each of the graphs. We discuss linear matrix inequalities that can be used to verify the condition guaranteeing spatial uniformity, and apply the result to a coupled oscillator network. Next we turn to reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous condition guaranteeing spatial uniformity of solutions. The paper contributes a relaxed condition to check spatial uniformity that allows individual components to have their own specific diffusion terms and interconnection structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
