Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used spatial/network autocorrelation models). The standard equilibrium solution to the diffusion model depends on strict timescale separation between network dynamics and attribute dynamics, such that the diffusion network can be considered fixed with respect to the diffusion process. Here, we consider a relaxation of this assumption, in which the network changes only slowly relative to the diffusion dynamics. In this case, we show that one can obtain a perturbative solution to the diffusion model, which depends on knowledge of past states in only a minimal way.

翻译：受多种名称指代且出现在多种情境中的受迫线性扩散模型，是社会网络内权力与影响力建模的核心模型（同时也是广泛使用的空间/网络自相关模型的机制基础）。该扩散模型的标准平衡解依赖于网络动态与属性动态之间严格的时间尺度分离，使得扩散网络可被视为相对于扩散过程固定不变。本文考虑放松这一假设，即网络相对于扩散动态仅缓慢变化。在此情况下，我们证明可获得扩散模型的微扰解，该解仅需以最小化方式依赖过去状态的信息。