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== 反应扩散过程 ==

==反应扩散过程==

[[File:Snipaste_2020-10-23_22-40-33.png|thumb|right|(a) Schematic illustration of the simplified modeling framework based on the particle-network scheme. At the macroscopic level the system is composed of a heterogeneous network of subpopulations. The contagion process in one subpopulation can spread to other subpopulations because of particles diffusing across subpopulations. (b) At the microscopic level, each subpopulation contains a population of individuals. The dynamical process, for instance, a contagion phenomenon, is described by a simple compartmentalization (compartments are indicated by different colored dots in the picture). Within each subpopulation, individuals can mix homogeneously or according to a subnetwork and can diffuse with probability p from one subpopulation to another following the edges of the network. (c) A critical value $p_c$ of the individuals or particles diffusion identifies a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected.]]  

[[File:Snipaste_2020-10-23_22-40-33.png|thumb|right|(a)基于粒子网络方案的简化建模框架示意图。在宏观层面上，系统是由一个异质性的亚种群网络组成。由于粒子在亚群间的扩散，一个亚群内的传染过程可以传播到其他亚群。(b)在微观水平上，每个亚种群包含一个个体种群。例如，动态过程，一种传染现象，可以用简单的划分来描述(图中不同颜色的点表示这些划分)。在每个子种群中，个体可以均匀地或根据一个子网络进行混合，并且可以沿着网络的边缘以概率<math>p</math>的方式从一个子种群扩散到另一个子种群。(c)个体或粒子扩散的临界值<math>p_c</math>确定了在传染影响系统的大部分和只影响一小部分的状态之间的相变。]]  

More in general models of social behavior and human mobility are often framed as reaction-diffusion processes where each node $i$ is allowed to host any nonnegative integer number of particles $\mathcal{N}(i)$, so that the total particle population of the system is $\mathcal{N}=\sum_i\mathcal{N}(i)$. This particle-network framework considers that each particle diffuses along the edges connecting nodes with a diffusion coefficient that depends on the node degree and/or other node attributes. Within each node particles may react according to different schemes characterizing the interaction dynamics of the system. A simple sketch of the particle-network framework is represented in the Figure.

More in general models of social behavior and human mobility are often framed as reaction-diffusion processes where each node $i$ is allowed to host any nonnegative integer number of particles $\mathcal{N}(i)$, so that the total particle population of the system is $\mathcal{N}=\sum_i\mathcal{N}(i)$. This particle-network framework considers that each particle diffuses along the edges connecting nodes with a diffusion coefficient that depends on the node degree and/or other node attributes. Within each node particles may react according to different schemes characterizing the interaction dynamics of the system. A simple sketch of the particle-network framework is represented in the Figure.